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solvefor b,a=cos(-1(a/(sqrt(a^2+b^2))))

解

解く

b, a = cos (- 1 (\frac{a}{a ^{2} + b ^{2}}))

解

b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

解答ステップ

a = cos (- 1 \cdot (\frac{a}{a ^{2} + b ^{2}}))

辺を交換する

cos (- 1 \cdot \frac{a}{a ^{2} + b ^{2}}) = a

三角関数の逆数プロパティを適用する

cos (- 1 \cdot \frac{a}{a ^{2} + b ^{2}}) = a

以下の一般解

cos (- 1 \frac{a}{a ^{2} + b ^{2}}) = a

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = - arccos (a) + 2 πn

- 1 \cdot \frac{a}{a ^{2} + b ^{2}} = arccos (a) + 2 πn, - 1 \cdot \frac{a}{a ^{2} + b ^{2}} = - arccos (a) + 2 πn

- 1 \cdot \frac{a}{a ^{2} + b ^{2}} = arccos (a) + 2 πn, - 1 \cdot \frac{a}{a ^{2} + b ^{2}} = - arccos (a) + 2 πn

解く

- 1 \cdot \frac{a}{a ^{2} + b ^{2}} = arccos (a) + 2 πn : b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

- 1 \cdot \frac{a}{a ^{2} + b ^{2}} = arccos (a) + 2 πn

拡張

- 1 \cdot \frac{a}{a ^{2} + b ^{2}} : - \frac{a}{a ^{2} + b ^{2}}

- 1 \cdot \frac{a}{a ^{2} + b ^{2}}

乗算:

1 \cdot \frac{a}{a ^{2} + b ^{2}} = \frac{a}{a ^{2} + b ^{2}}

= - \frac{a}{a ^{2} + b ^{2}}

- \frac{a}{a ^{2} + b ^{2}} = arccos (a) + 2 πn

両辺を2乗する:

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}

- \frac{a}{a ^{2} + b ^{2}} = arccos (a) + 2 πn

(- \frac{a}{a ^{2} + b ^{2}})^{2} = (arccos (a) + 2 πn)^{2}

拡張

(- \frac{a}{a ^{2} + b ^{2}})^{2} : \frac{a ^{2}}{a ^{2} + b ^{2}}

(- \frac{a}{a ^{2} + b ^{2}})^{2}

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- \frac{a}{a ^{2} + b ^{2}})^{2} = (\frac{a}{a ^{2} + b ^{2}})^{2}

= (\frac{a}{a ^{2} + b ^{2}})^{2}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{a ^{2}}{( a ^{2} + b ^{2} ) ^{2}}

(a^{2} + b^{2})^{2} : a^{2} + b^{2}

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= ((a^{2} + b^{2})^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (a^{2} + b^{2})^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= a^{2} + b^{2}

= \frac{a ^{2}}{a ^{2} + b ^{2}}

拡張

(arccos (a) + 2 πn)^{2} : arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}

(arccos (a) + 2 πn)^{2}

完全平方式を適用する:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = arccos (a), b = 2 πn

= arccos^{2} (a) + 2 arccos (a) \cdot 2 πn + (2 πn)^{2}

簡素化

arccos^{2} (a) + 2 arccos (a) \cdot 2 πn + (2 πn)^{2} : arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}

arccos^{2} (a) + 2 arccos (a) \cdot 2 πn + (2 πn)^{2}

2 arccos (a) \cdot 2 πn = 4 πn arccos (a)

2 arccos (a) \cdot 2 πn

数を乗じる:

2 \cdot 2 = 4

= 4 πn arccos (a)

(2 πn)^{2} = 4 π^{2} n^{2}

(2 πn)^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{2} π^{2} n^{2}

2^{2} = 4

= 4 π^{2} n^{2}

= arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}

= arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}

解く

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2} : b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}

以下で両辺を乗じる:

a^{2} + b^{2}

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}

以下で両辺を乗じる:

a^{2} + b^{2}

\frac{a ^{2}}{a ^{2} + b ^{2}} (a^{2} + b^{2}) = arccos^{2} (a) (a^{2} + b^{2}) + 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2})

簡素化

a^{2} = arccos^{2} (a) (a^{2} + b^{2}) + 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2})

a^{2} = arccos^{2} (a) (a^{2} + b^{2}) + 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2})

解く

a^{2} = arccos^{2} (a) (a^{2} + b^{2}) + 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2}) : b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

a^{2} = arccos^{2} (a) (a^{2} + b^{2}) + 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2})

辺を交換する

arccos^{2} (a) (a^{2} + b^{2}) + 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2}) = a^{2}

拡張

arccos^{2} (a) (a^{2} + b^{2}) : a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2}

arccos^{2} (a) (a^{2} + b^{2})

分配法則を適用する:

a (b + c) = ab + a c

a = arccos^{2} (a), b = a^{2}, c = b^{2}

= arccos^{2} (a) a^{2} + arccos^{2} (a) b^{2}

= a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2}

a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2} + 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2}) = a^{2}

拡張

4 πn arccos (a) (a^{2} + b^{2}) : 4 π a^{2} n arccos (a) + 4 πn arccos (a) b^{2}

4 πn arccos (a) (a^{2} + b^{2})

分配法則を適用する:

a (b + c) = ab + a c

a = 4 πn arccos (a), b = a^{2}, c = b^{2}

= 4 πn arccos (a) a^{2} + 4 πn arccos (a) b^{2}

= 4 π a^{2} n arccos (a) + 4 πn arccos (a) b^{2}

a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2} + 4 π a^{2} n arccos (a) + 4 πn arccos (a) b^{2} + 4 π^{2} n^{2} (a^{2} + b^{2}) = a^{2}

拡張

4 π^{2} n^{2} (a^{2} + b^{2}) : 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2}

4 π^{2} n^{2} (a^{2} + b^{2})

分配法則を適用する:

a (b + c) = ab + a c

a = 4 π^{2} n^{2}, b = a^{2}, c = b^{2}

= 4 π^{2} n^{2} a^{2} + 4 π^{2} n^{2} b^{2}

= 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2}

a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2} + 4 π a^{2} n arccos (a) + 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2}

a^{2} arccos^{2} (a)

を右側に移動します

a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2} + 4 π a^{2} n arccos (a) + 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2}

両辺から

a^{2} arccos^{2} (a)

を引く

a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2} + 4 π a^{2} n arccos (a) + 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} - a^{2} arccos^{2} (a) = a^{2} - a^{2} arccos^{2} (a)

簡素化

arccos^{2} (a) b^{2} + 4 π a^{2} n arccos (a) + 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a)

arccos^{2} (a) b^{2} + 4 π a^{2} n arccos (a) + 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a)

4 π a^{2} n arccos (a)

を右側に移動します

arccos^{2} (a) b^{2} + 4 π a^{2} n arccos (a) + 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a)

両辺から

4 π a^{2} n arccos (a)

を引く

arccos^{2} (a) b^{2} + 4 π a^{2} n arccos (a) + 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} - 4 π a^{2} n arccos (a) = a^{2} - a^{2} arccos^{2} (a) - 4 π a^{2} n arccos (a)

簡素化

arccos^{2} (a) b^{2} + 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a) - 4 π a^{2} n arccos (a)

arccos^{2} (a) b^{2} + 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a) - 4 π a^{2} n arccos (a)

4 π^{2} a^{2} n^{2}

を右側に移動します

arccos^{2} (a) b^{2} + 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a) - 4 π a^{2} n arccos (a)

両辺から

4 π^{2} a^{2} n^{2}

を引く

arccos^{2} (a) b^{2} + 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} - 4 π^{2} a^{2} n^{2} = a^{2} - a^{2} arccos^{2} (a) - 4 π a^{2} n arccos (a) - 4 π^{2} a^{2} n^{2}

簡素化

arccos^{2} (a) b^{2} + 4 πn arccos (a) b^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a) - 4 π a^{2} n arccos (a) - 4 π^{2} a^{2} n^{2}

arccos^{2} (a) b^{2} + 4 πn arccos (a) b^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a) - 4 π a^{2} n arccos (a) - 4 π^{2} a^{2} n^{2}

因数

arccos^{2} (a) b^{2} + 4 πn arccos (a) b^{2} + 4 π^{2} n^{2} b^{2} : b^{2} (arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2})

arccos^{2} (a) b^{2} + 4 πn arccos (a) b^{2} + 4 π^{2} n^{2} b^{2}

共通項をくくり出す

b^{2}

= b^{2} (arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2})

b^{2} (arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}) = a^{2} - a^{2} arccos^{2} (a) - 4 π a^{2} n arccos (a) - 4 π^{2} a^{2} n^{2}

以下で両辺を割る

arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}

b^{2} (arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}) = a^{2} - a^{2} arccos^{2} (a) - 4 π a^{2} n arccos (a) - 4 π^{2} a^{2} n^{2}

以下で両辺を割る

arccos^{2} (a) + 4 πn arccos (a) + 4 π^{2} n^{2}

\frac{b ^{2} ( arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2} )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} = \frac{a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

簡素化

b^{2} = \frac{a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

b^{2} = \frac{a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

b = \frac{a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

簡素化

\frac{a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} : \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

\frac{a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

分数を組み合わせる

\frac{a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 πn a ^{2} arccos ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} : \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

規則を適用

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

= \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 π a ^{2} n arccos ( a ) - 4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

= \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

簡素化

- \frac{a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} : - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

- \frac{a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

分数を組み合わせる

\frac{a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 πn a ^{2} arccos ( a )}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} : \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

規則を適用

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

= - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

解く

- 1 \cdot \frac{a}{a ^{2} + b ^{2}} = - arccos (a) + 2 πn : b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

- 1 \cdot \frac{a}{a ^{2} + b ^{2}} = - arccos (a) + 2 πn

拡張

- 1 \cdot \frac{a}{a ^{2} + b ^{2}} : - \frac{a}{a ^{2} + b ^{2}}

- 1 \cdot \frac{a}{a ^{2} + b ^{2}}

乗算:

1 \cdot \frac{a}{a ^{2} + b ^{2}} = \frac{a}{a ^{2} + b ^{2}}

= - \frac{a}{a ^{2} + b ^{2}}

- \frac{a}{a ^{2} + b ^{2}} = - arccos (a) + 2 πn

両辺を2乗する:

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}

- \frac{a}{a ^{2} + b ^{2}} = - arccos (a) + 2 πn

(- \frac{a}{a ^{2} + b ^{2}})^{2} = (- arccos (a) + 2 πn)^{2}

拡張

(- \frac{a}{a ^{2} + b ^{2}})^{2} : \frac{a ^{2}}{a ^{2} + b ^{2}}

(- \frac{a}{a ^{2} + b ^{2}})^{2}

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- \frac{a}{a ^{2} + b ^{2}})^{2} = (\frac{a}{a ^{2} + b ^{2}})^{2}

= (\frac{a}{a ^{2} + b ^{2}})^{2}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{a ^{2}}{( a ^{2} + b ^{2} ) ^{2}}

(a^{2} + b^{2})^{2} : a^{2} + b^{2}

累乗根の規則を適用する:

a = a^{\frac{1}{2}}

= ((a^{2} + b^{2})^{\frac{1}{2}})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (a^{2} + b^{2})^{\frac{1}{2} \cdot 2}

\frac{1}{2} \cdot 2 = 1

\frac{1}{2} \cdot 2

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 2}{2}

共通因数を約分する:

2

= 1

= a^{2} + b^{2}

= \frac{a ^{2}}{a ^{2} + b ^{2}}

拡張

(- arccos (a) + 2 πn)^{2} : arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}

(- arccos (a) + 2 πn)^{2}

完全平方式を適用する:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

a = - arccos (a), b = 2 πn

= (- arccos (a))^{2} + 2 (- arccos (a)) \cdot 2 πn + (2 πn)^{2}

簡素化

(- arccos (a))^{2} + 2 (- arccos (a)) \cdot 2 πn + (2 πn)^{2} : arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}

(- arccos (a))^{2} + 2 (- arccos (a)) \cdot 2 πn + (2 πn)^{2}

括弧を削除する:

(- a) = - a

= (- arccos (a))^{2} - 2 arccos (a) \cdot 2 πn + (2 πn)^{2}

(- arccos (a))^{2} = arccos^{2} (a)

(- arccos (a))^{2}

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

(- arccos (a))^{2} = arccos^{2} (a)

= arccos^{2} (a)

2 arccos (a) \cdot 2 πn = 4 πn arccos (a)

2 arccos (a) \cdot 2 πn

数を乗じる:

2 \cdot 2 = 4

= 4 πn arccos (a)

(2 πn)^{2} = 4 π^{2} n^{2}

(2 πn)^{2}

指数の規則を適用する:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{2} π^{2} n^{2}

2^{2} = 4

= 4 π^{2} n^{2}

= arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}

= arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}

解く

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2} : b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}

以下で両辺を乗じる:

a^{2} + b^{2}

\frac{a ^{2}}{a ^{2} + b ^{2}} = arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}

以下で両辺を乗じる:

a^{2} + b^{2}

\frac{a ^{2}}{a ^{2} + b ^{2}} (a^{2} + b^{2}) = arccos^{2} (a) (a^{2} + b^{2}) - 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2})

簡素化

a^{2} = arccos^{2} (a) (a^{2} + b^{2}) - 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2})

a^{2} = arccos^{2} (a) (a^{2} + b^{2}) - 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2})

解く

a^{2} = arccos^{2} (a) (a^{2} + b^{2}) - 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2}) : b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

a^{2} = arccos^{2} (a) (a^{2} + b^{2}) - 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2})

辺を交換する

arccos^{2} (a) (a^{2} + b^{2}) - 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2}) = a^{2}

拡張

arccos^{2} (a) (a^{2} + b^{2}) : a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2}

arccos^{2} (a) (a^{2} + b^{2})

分配法則を適用する:

a (b + c) = ab + a c

a = arccos^{2} (a), b = a^{2}, c = b^{2}

= arccos^{2} (a) a^{2} + arccos^{2} (a) b^{2}

= a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2}

a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2} - 4 πn arccos (a) (a^{2} + b^{2}) + 4 π^{2} n^{2} (a^{2} + b^{2}) = a^{2}

拡張

- 4 πn arccos (a) (a^{2} + b^{2}) : - 4 π a^{2} n arccos (a) - 4 πn arccos (a) b^{2}

- 4 πn arccos (a) (a^{2} + b^{2})

分配法則を適用する:

a (b + c) = ab + a c

a = - 4 πn arccos (a), b = a^{2}, c = b^{2}

= - 4 πn arccos (a) a^{2} + (- 4 πn arccos (a)) b^{2}

マイナス・プラスの規則を適用する

+ (- a) = - a

= - 4 π a^{2} n arccos (a) - 4 πn arccos (a) b^{2}

a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2} - 4 π a^{2} n arccos (a) - 4 πn arccos (a) b^{2} + 4 π^{2} n^{2} (a^{2} + b^{2}) = a^{2}

拡張

4 π^{2} n^{2} (a^{2} + b^{2}) : 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2}

4 π^{2} n^{2} (a^{2} + b^{2})

分配法則を適用する:

a (b + c) = ab + a c

a = 4 π^{2} n^{2}, b = a^{2}, c = b^{2}

= 4 π^{2} n^{2} a^{2} + 4 π^{2} n^{2} b^{2}

= 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2}

a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2} - 4 π a^{2} n arccos (a) - 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2}

a^{2} arccos^{2} (a)

を右側に移動します

a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2} - 4 π a^{2} n arccos (a) - 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2}

両辺から

a^{2} arccos^{2} (a)

を引く

a^{2} arccos^{2} (a) + arccos^{2} (a) b^{2} - 4 π a^{2} n arccos (a) - 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} - a^{2} arccos^{2} (a) = a^{2} - a^{2} arccos^{2} (a)

簡素化

arccos^{2} (a) b^{2} - 4 π a^{2} n arccos (a) - 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a)

arccos^{2} (a) b^{2} - 4 π a^{2} n arccos (a) - 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a)

4 π a^{2} n arccos (a)

を右側に移動します

arccos^{2} (a) b^{2} - 4 π a^{2} n arccos (a) - 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a)

両辺に

4 π a^{2} n arccos (a)

を足す

arccos^{2} (a) b^{2} - 4 π a^{2} n arccos (a) - 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} + 4 π a^{2} n arccos (a) = a^{2} - a^{2} arccos^{2} (a) + 4 π a^{2} n arccos (a)

簡素化

arccos^{2} (a) b^{2} - 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a) + 4 π a^{2} n arccos (a)

arccos^{2} (a) b^{2} - 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a) + 4 π a^{2} n arccos (a)

4 π^{2} a^{2} n^{2}

を右側に移動します

arccos^{2} (a) b^{2} - 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a) + 4 π a^{2} n arccos (a)

両辺から

4 π^{2} a^{2} n^{2}

を引く

arccos^{2} (a) b^{2} - 4 πn arccos (a) b^{2} + 4 π^{2} a^{2} n^{2} + 4 π^{2} n^{2} b^{2} - 4 π^{2} a^{2} n^{2} = a^{2} - a^{2} arccos^{2} (a) + 4 π a^{2} n arccos (a) - 4 π^{2} a^{2} n^{2}

簡素化

arccos^{2} (a) b^{2} - 4 πn arccos (a) b^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a) + 4 π a^{2} n arccos (a) - 4 π^{2} a^{2} n^{2}

arccos^{2} (a) b^{2} - 4 πn arccos (a) b^{2} + 4 π^{2} n^{2} b^{2} = a^{2} - a^{2} arccos^{2} (a) + 4 π a^{2} n arccos (a) - 4 π^{2} a^{2} n^{2}

因数

arccos^{2} (a) b^{2} - 4 πn arccos (a) b^{2} + 4 π^{2} n^{2} b^{2} : b^{2} (arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2})

arccos^{2} (a) b^{2} - 4 πn arccos (a) b^{2} + 4 π^{2} n^{2} b^{2}

共通項をくくり出す

b^{2}

= b^{2} (arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2})

b^{2} (arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}) = a^{2} - a^{2} arccos^{2} (a) + 4 π a^{2} n arccos (a) - 4 π^{2} a^{2} n^{2}

以下で両辺を割る

arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}

b^{2} (arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}) = a^{2} - a^{2} arccos^{2} (a) + 4 π a^{2} n arccos (a) - 4 π^{2} a^{2} n^{2}

以下で両辺を割る

arccos^{2} (a) - 4 πn arccos (a) + 4 π^{2} n^{2}

\frac{b ^{2} ( arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2} )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} = \frac{a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} + \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

簡素化

b^{2} = \frac{a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} + \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

b^{2} = \frac{a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} + \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

b = \frac{a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} + \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} + \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

簡素化

\frac{a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} + \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} : \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

\frac{a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} + \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

分数を組み合わせる

\frac{a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} + \frac{4 πn a ^{2} arccos ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} : \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

規則を適用

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

= \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 π a ^{2} n arccos ( a ) - 4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

= \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

簡素化

- \frac{a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} + \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} : - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

- \frac{a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} + \frac{4 π a ^{2} n arccos ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} a ^{2} n ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

分数を組み合わせる

\frac{a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{a ^{2} arccos ^{2} ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} + \frac{4 πn a ^{2} arccos ( a )}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} - \frac{4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}} : \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

規則を適用

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

= - \frac{a ^{2} + 4 πn a ^{2} arccos ( a ) - a ^{2} arccos ^{2} ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

= - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) - 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) + 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}, b = - \frac{a ^{2} - a ^{2} arccos ^{2} ( a ) + 4 πn a ^{2} arccos ( a ) - 4 π ^{2} n ^{2} a ^{2}}{arccos ^{2} ( a ) - 4 πn arccos ( a ) + 4 π ^{2} n ^{2}}

人気の例

(1/2 sin(2x))^2= 1/4 sin^2(4x)

(\frac{1}{2} sin (2 x))^{2} = \frac{1}{4} sin^{2} (4 x)

8sin^2(x)-3sin(x)-2=0

8 sin^{2} (x) - 3 sin (x) - 2 = 0

2sin^2(x)3=7sin(x),0<= x<= 2pi

2 sin^{2} (x) 3 = 7 sin (x), 0 \leq x \leq 2 π

6 sin (x) + 12 = 15

cot^2(x)cos(x)=cos(x)

cot^{2} (x) cos (x) = cos (x)