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受欢迎的三角函数 >

3sec^2(x)=sec(x)

解答

3 sec^{2} (x) = sec (x)

解答

x \in R 无解

求解步骤

3 sec^{2} (x) = sec (x)

用替代法求解

3 sec^{2} (x) = sec (x)

令

: sec (x) = u

3 u^{2} = u

3 u^{2} = u : u = \frac{1}{3}, u = 0

3 u^{2} = u

将

u

para o lado esquerdo

3 u^{2} = u

两边减去

u

3 u^{2} - u = u - u

化简

3 u^{2} - u = 0

3 u^{2} - u = 0

使用求根公式求解

3 u^{2} - u = 0

二次方程求根公式:

若

a = 3, b = - 1, c = 0

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

u_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 3 \cdot 0}{2 \cdot 3}

(- 1)^{2} - 4 \cdot 3 \cdot 0 = 1

(- 1)^{2} - 4 \cdot 3 \cdot 0

(- 1)^{2} = 1

(- 1)^{2}

使用指数法则:

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

若

n

是偶数

(- 1)^{2} = 1^{2}

= 1^{2}

使用法则

1^{a} = 1

= 1

4 \cdot 3 \cdot 0 = 0

4 \cdot 3 \cdot 0

使用法则

0 \cdot a = 0

= 0

= 1 - 0

数字相减:

1 - 0 = 1

= 1

使用法则

1 = 1

= 1

u_{1, 2} = \frac{- ( - 1 ) \pm 1}{2 \cdot 3}

将解分隔开

u_{1} = \frac{- ( - 1 ) + 1}{2 \cdot 3}, u_{2} = \frac{- ( - 1 ) - 1}{2 \cdot 3}

u = \frac{- ( - 1 ) + 1}{2 \cdot 3} : \frac{1}{3}

\frac{- ( - 1 ) + 1}{2 \cdot 3}

使用法则

- (- a) = a

= \frac{1 + 1}{2 \cdot 3}

数字相加:

1 + 1 = 2

= \frac{2}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{2}{6}

约分:

2

= \frac{1}{3}

u = \frac{- ( - 1 ) - 1}{2 \cdot 3} : 0

\frac{- ( - 1 ) - 1}{2 \cdot 3}

使用法则

- (- a) = a

= \frac{1 - 1}{2 \cdot 3}

数字相减:

1 - 1 = 0

= \frac{0}{2 \cdot 3}

数字相乘:

2 \cdot 3 = 6

= \frac{0}{6}

使用法则

\frac{0}{a} = 0, a \neq = 0

= 0

二次方程组的解是:

u = \frac{1}{3}, u = 0

u = sec (x)

代回

sec (x) = \frac{1}{3}, sec (x) = 0

sec (x) = \frac{1}{3}, sec (x) = 0

sec (x) = \frac{1}{3} :

无解

sec (x) = \frac{1}{3}

sec (x) \leq - 1 or sec (x) \geq 1

无解

sec (x) = 0 :

无解

sec (x) = 0

sec (x) \leq - 1 or sec (x) \geq 1

无解

合并所有解

x \in R 无解

作图

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