What is the general solution for cos(x+10)-cos(x+90)=1 ?

The general solution for cos(x+10)-cos(x+90)=1 is x=-50+360n+0.89125…,x=130+360n-0.89125…

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cos(x+10)-cos(x+90)=1

Solution

cos (x + 1 0^{\circ}) - cos (x + 9 0^{\circ}) = 1

Solution

x = - 5 0^{\circ} + 36 0^{\circ} n + 0.89125 \dots, x = 13 0^{\circ} + 36 0^{\circ} n - 0.89125 \dots

Radians

x = - \frac{5 π}{18} + 0.89125 \dots + 2 πn, x = \frac{13 π}{18} - 0.89125 \dots + 2 πn

Solution steps

cos (x + 1 0^{\circ}) - cos (x + 9 0^{\circ}) = 1

Rewrite using trig identities

cos (x + 1 0^{\circ}) - cos (x + 9 0^{\circ})

Use the Sum to Product identity:

cos (s) - cos (t) = - 2 sin (\frac{s + t}{2}) sin (\frac{s - t}{2})

= - 2 sin (\frac{x + 1 0 ^{\circ} + x + 9 0 ^{\circ}}{2}) sin (\frac{x + 1 0 ^{\circ} - ( x + 9 0 ^{\circ} )}{2})

Simplify

- 2 sin (\frac{x + 1 0 ^{\circ} + x + 9 0 ^{\circ}}{2}) sin (\frac{x + 1 0 ^{\circ} - ( x + 9 0 ^{\circ} )}{2}) : 2 sin (4 0^{\circ}) sin (\frac{18 x + 90 0 ^{\circ}}{18})

- 2 sin (\frac{x + 1 0 ^{\circ} + x + 9 0 ^{\circ}}{2}) sin (\frac{x + 1 0 ^{\circ} - ( x + 9 0 ^{\circ} )}{2})

\frac{x + 1 0 ^{\circ} + x + 9 0 ^{\circ}}{2} = \frac{18 x + 90 0 ^{\circ}}{18}

\frac{x + 1 0 ^{\circ} + x + 9 0 ^{\circ}}{2}

x + 1 0^{\circ} + x + 9 0^{\circ} = 2 x + 9 0^{\circ} + 1 0^{\circ}

x + 1 0^{\circ} + x + 9 0^{\circ}

Group like terms

= x + x + 9 0^{\circ} + 1 0^{\circ}

Add similar elements:

x + x = 2 x

= 2 x + 9 0^{\circ} + 1 0^{\circ}

= \frac{2 x + 9 0 ^{\circ} + 1 0 ^{\circ}}{2}

Join

2 x + 9 0^{\circ} + 1 0^{\circ} : \frac{18 x + 90 0 ^{\circ}}{9}

2 x + 9 0^{\circ} + 1 0^{\circ}

Convert element to fraction:

2 x = \frac{2 x}{1}

= \frac{2 x}{1} + 9 0^{\circ} + 1 0^{\circ}

Least Common Multiplier of

1, 2, 18 : 18

1, 2, 18

Least Common Multiplier (LCM)

Prime factorization of

1

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

18 : 2 \cdot 3 \cdot 3

18

18

divides by

218 = 9 \cdot 2

= 2 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 3

Compute a number comprised of factors that appear in at least one of the following:

1, 2, 18

= 2 \cdot 3 \cdot 3

Multiply the numbers:

2 \cdot 3 \cdot 3 = 18

= 18

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

18

For

\frac{2 x}{1} :

multiply the denominator and numerator by

18

\frac{2 x}{1} = \frac{2 x \cdot 18}{1 \cdot 18} = \frac{36 x}{18}

For

9 0^{\circ} :

multiply the denominator and numerator by

9

9 0^{\circ} = \frac{18 0 ^{\circ} 9}{2 \cdot 9} = 9 0^{\circ}

= \frac{36 x}{18} + 9 0^{\circ} + 1 0^{\circ}

Since the denominators are equal, combine the fractions:

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

= \frac{36 x + 18 0 ^{\circ} 9 + 18 0 ^{\circ}}{18}

Add similar elements:

162 0^{\circ} + 18 0^{\circ} = 180 0^{\circ}

= \frac{36 x + 180 0 ^{\circ}}{18}

Factor

36 x + 180 0^{\circ} : 2 (18 x + 90 0^{\circ})

36 x + 180 0^{\circ}

Rewrite as

= 2 \cdot 18 x + 2 \cdot 90 0^{\circ}

Factor out common term

2

= 2 (18 x + 90 0^{\circ})

= \frac{2 ( 18 x + 90 0 ^{\circ} )}{18}

Cancel the common factor:

2

= \frac{18 x + 90 0 ^{\circ}}{9}

= \frac{\frac{18 x + 90 0 ^{\circ}}{9}}{2}

Apply the fraction rule:

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

= \frac{18 x + 90 0 ^{\circ}}{9 \cdot 2}

Multiply the numbers:

9 \cdot 2 = 18

= \frac{18 x + 90 0 ^{\circ}}{18}

= - 2 sin (\frac{18 x + 90 0 ^{\circ}}{18}) sin (\frac{x - ( x + 9 0 ^{\circ} ) + 1 0 ^{\circ}}{2})

\frac{x + 1 0 ^{\circ} - ( x + 9 0 ^{\circ} )}{2} = - 4 0^{\circ}

\frac{x + 1 0 ^{\circ} - ( x + 9 0 ^{\circ} )}{2}

Join

x + 1 0^{\circ} - (x + 9 0^{\circ}) : - 8 0^{\circ}

x + 1 0^{\circ} - (x + 9 0^{\circ})

Convert element to fraction:

x = \frac{x 18}{18}, (x + 9 0^{\circ}) = \frac{( x + 9 0 ^{\circ} ) 18}{18}

= \frac{x \cdot 18}{18} + 1 0^{\circ} - \frac{( x + 9 0 ^{\circ} ) \cdot 18}{18}

Since the denominators are equal, combine the fractions:

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

= \frac{x \cdot 18 + 18 0 ^{\circ} - ( x + 9 0 ^{\circ} ) \cdot 18}{18}

Expand

x \cdot 18 + 18 0^{\circ} - (x + 9 0^{\circ}) \cdot 18 : - 144 0^{\circ}

x \cdot 18 + 18 0^{\circ} - (x + 9 0^{\circ}) \cdot 18

= 18 x + 18 0^{\circ} - 18 (x + 9 0^{\circ})

Expand

- 18 (x + 9 0^{\circ}) : - 18 x - 162 0^{\circ}

- 18 (x + 9 0^{\circ})

Apply the distributive law:

a (b + c) = ab + a c

a = - 18, b = x, c = 9 0^{\circ}

= - 18 x + (- 18) 9 0^{\circ}

Apply minus-plus rules

+ (- a) = - a

= - 18 x - 18 \cdot 9 0^{\circ}

18 \cdot 9 0^{\circ} = 162 0^{\circ}

18 \cdot 9 0^{\circ}

Multiply fractions:

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

= 162 0^{\circ}

Divide the numbers:

\frac{18}{2} = 9

= 162 0^{\circ}

= - 18 x - 162 0^{\circ}

= x \cdot 18 + 18 0^{\circ} - 18 x - 162 0^{\circ}

Simplify

x \cdot 18 + 18 0^{\circ} - 18 x - 162 0^{\circ} : - 144 0^{\circ}

x \cdot 18 + 18 0^{\circ} - 18 x - 162 0^{\circ}

Group like terms

= 18 x - 18 x + 18 0^{\circ} - 162 0^{\circ}

Add similar elements:

18 x - 18 x = 0

= 18 0^{\circ} - 162 0^{\circ}

Add similar elements:

18 0^{\circ} - 162 0^{\circ} = - 144 0^{\circ}

= - 144 0^{\circ}

= - 144 0^{\circ}

= \frac{- 144 0 ^{\circ}}{18}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - 8 0^{\circ}

Cancel the common factor:

2

= - 8 0^{\circ}

= \frac{- 8 0 ^{\circ}}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{8 0 ^{\circ}}{2}

Apply the fraction rule:

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

\frac{8 0 ^{\circ}}{2} = \frac{72 0 ^{\circ}}{9 \cdot 2}

= - \frac{72 0 ^{\circ}}{9 \cdot 2}

Multiply the numbers:

9 \cdot 2 = 18

= - 4 0^{\circ}

Cancel the common factor:

2

= - 4 0^{\circ}

= - 2 sin (- 4 0^{\circ}) sin (\frac{18 x + 90 0 ^{\circ}}{18})

Simplify

sin (- 4 0^{\circ}) : - sin (4 0^{\circ})

sin (- 4 0^{\circ})

Use the following property:

sin (- x) = - sin (x)

sin (- 4 0^{\circ}) = - sin (4 0^{\circ})

= - sin (4 0^{\circ})

= - 2 (- sin (4 0^{\circ})) sin (\frac{18 x + 90 0 ^{\circ}}{18})

Apply rule

- (- a) = a

= 2 sin (\frac{18 x + 90 0 ^{\circ}}{18}) sin (4 0^{\circ})

= 2 sin (4 0^{\circ}) sin (\frac{18 x + 90 0 ^{\circ}}{18})

2 sin (4 0^{\circ}) sin (\frac{18 x + 90 0 ^{\circ}}{18}) = 1

Divide both sides by

2 sin (4 0^{\circ})

2 sin (4 0^{\circ}) sin (\frac{18 x + 90 0 ^{\circ}}{18}) = 1

Divide both sides by

2 sin (4 0^{\circ})

\frac{2 sin ( 4 0 ^{\circ} ) sin ( \frac{18 x + 90 0 ^{\circ}}{18} )}{2 sin ( 4 0 ^{\circ} )} = \frac{1}{2 sin ( 4 0 ^{\circ} )}

Simplify

sin (\frac{18 x + 90 0 ^{\circ}}{18}) = \frac{1}{2 sin ( 4 0 ^{\circ} )}

sin (\frac{18 x + 90 0 ^{\circ}}{18}) = \frac{1}{2 sin ( 4 0 ^{\circ} )}

Apply trig inverse properties

sin (\frac{18 x + 90 0 ^{\circ}}{18}) = \frac{1}{2 sin ( 4 0 ^{\circ} )}

General solutions for

sin (\frac{18 x + 90 0 ^{\circ}}{18}) = \frac{1}{2 sin ( 4 0 ^{\circ} )}

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

\frac{18 x + 90 0 ^{\circ}}{18} = arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 36 0^{\circ} n, \frac{18 x + 90 0 ^{\circ}}{18} = 18 0^{\circ} - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 36 0^{\circ} n

\frac{18 x + 90 0 ^{\circ}}{18} = arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 36 0^{\circ} n, \frac{18 x + 90 0 ^{\circ}}{18} = 18 0^{\circ} - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 36 0^{\circ} n

Solve

\frac{18 x + 90 0 ^{\circ}}{18} = arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 36 0^{\circ} n : x = - 5 0^{\circ} + 36 0^{\circ} n + arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

\frac{18 x + 90 0 ^{\circ}}{18} = arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 36 0^{\circ} n

Multiply both sides by

18

\frac{18 x + 90 0 ^{\circ}}{18} = arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 36 0^{\circ} n

Multiply both sides by

18

\frac{18 ( 18 x + 90 0 ^{\circ} )}{18} = 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 18 \cdot 36 0^{\circ} n

Simplify

\frac{18 ( 18 x + 90 0 ^{\circ} )}{18} = 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 18 \cdot 36 0^{\circ} n

Simplify

\frac{18 ( 18 x + 90 0 ^{\circ} )}{18} : 18 x + 90 0^{\circ}

\frac{18 ( 18 x + 90 0 ^{\circ} )}{18}

Divide the numbers:

\frac{18}{18} = 1

= 18 x + 90 0^{\circ}

Simplify

18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 18 \cdot 36 0^{\circ} n : 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 18 \cdot 36 0^{\circ} n

Multiply the numbers:

18 \cdot 2 = 36

= 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

18 x + 90 0^{\circ} = 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

18 x + 90 0^{\circ} = 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

18 x + 90 0^{\circ} = 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

Move

90 0^{\circ}

to the right side

18 x + 90 0^{\circ} = 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

Subtract

90 0^{\circ}

from both sides

18 x + 90 0^{\circ} - 90 0^{\circ} = 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n - 90 0^{\circ}

Simplify

18 x = 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n - 90 0^{\circ}

18 x = 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n - 90 0^{\circ}

Divide both sides by

18

18 x = 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n - 90 0^{\circ}

Divide both sides by

18

\frac{18 x}{18} = \frac{18 arcsin ( \frac{1}{2 s i n ( 4 0 ^{\circ} )} )}{18} + \frac{648 0 ^{\circ} n}{18} - 5 0^{\circ}

Simplify

\frac{18 x}{18} = \frac{18 arcsin ( \frac{1}{2 s i n ( 4 0 ^{\circ} )} )}{18} + \frac{648 0 ^{\circ} n}{18} - 5 0^{\circ}

Simplify

\frac{18 x}{18} : x

\frac{18 x}{18}

Divide the numbers:

\frac{18}{18} = 1

= x

Simplify

\frac{18 arcsin ( \frac{1}{2 s i n ( 4 0 ^{\circ} )} )}{18} + \frac{648 0 ^{\circ} n}{18} - 5 0^{\circ} : - 5 0^{\circ} + 36 0^{\circ} n + arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

\frac{18 arcsin ( \frac{1}{2 s i n ( 4 0 ^{\circ} )} )}{18} + \frac{648 0 ^{\circ} n}{18} - 5 0^{\circ}

Group like terms

= - 5 0^{\circ} + \frac{648 0 ^{\circ} n}{18} + \frac{18 arcsin ( \frac{1}{2 s i n ( 4 0 ^{\circ} )} )}{18}

Divide the numbers:

\frac{36}{18} = 2

= - 5 0^{\circ} + 36 0^{\circ} n + \frac{18 arcsin ( \frac{1}{2 s i n ( 4 0 ^{\circ} )} )}{18}

Divide the numbers:

\frac{18}{18} = 1

= - 5 0^{\circ} + 36 0^{\circ} n + arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

x = - 5 0^{\circ} + 36 0^{\circ} n + arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

x = - 5 0^{\circ} + 36 0^{\circ} n + arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

x = - 5 0^{\circ} + 36 0^{\circ} n + arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

Solve

\frac{18 x + 90 0 ^{\circ}}{18} = 18 0^{\circ} - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 36 0^{\circ} n : x = 13 0^{\circ} + 36 0^{\circ} n - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

\frac{18 x + 90 0 ^{\circ}}{18} = 18 0^{\circ} - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 36 0^{\circ} n

Multiply both sides by

18

\frac{18 x + 90 0 ^{\circ}}{18} = 18 0^{\circ} - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 36 0^{\circ} n

Multiply both sides by

18

\frac{18 ( 18 x + 90 0 ^{\circ} )}{18} = 324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 18 \cdot 36 0^{\circ} n

Simplify

\frac{18 ( 18 x + 90 0 ^{\circ} )}{18} = 324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 18 \cdot 36 0^{\circ} n

Simplify

\frac{18 ( 18 x + 90 0 ^{\circ} )}{18} : 18 x + 90 0^{\circ}

\frac{18 ( 18 x + 90 0 ^{\circ} )}{18}

Divide the numbers:

\frac{18}{18} = 1

= 18 x + 90 0^{\circ}

Simplify

324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 18 \cdot 36 0^{\circ} n : 324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 18 \cdot 36 0^{\circ} n

Multiply the numbers:

18 \cdot 2 = 36

= 324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

18 x + 90 0^{\circ} = 324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

18 x + 90 0^{\circ} = 324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

18 x + 90 0^{\circ} = 324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

Move

90 0^{\circ}

to the right side

18 x + 90 0^{\circ} = 324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n

Subtract

90 0^{\circ}

from both sides

18 x + 90 0^{\circ} - 90 0^{\circ} = 324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n - 90 0^{\circ}

Simplify

18 x + 90 0^{\circ} - 90 0^{\circ} = 324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n - 90 0^{\circ}

Simplify

18 x + 90 0^{\circ} - 90 0^{\circ} : 18 x

18 x + 90 0^{\circ} - 90 0^{\circ}

Add similar elements:

90 0^{\circ} - 90 0^{\circ} = 0

= 18 x

Simplify

324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n - 90 0^{\circ} : 234 0^{\circ} + 648 0^{\circ} n - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

324 0^{\circ} - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}) + 648 0^{\circ} n - 90 0^{\circ}

Group like terms

= 324 0^{\circ} - 90 0^{\circ} + 648 0^{\circ} n - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

Add similar elements:

324 0^{\circ} - 90 0^{\circ} = 234 0^{\circ}

= 234 0^{\circ} + 648 0^{\circ} n - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

18 x = 234 0^{\circ} + 648 0^{\circ} n - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

18 x = 234 0^{\circ} + 648 0^{\circ} n - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

18 x = 234 0^{\circ} + 648 0^{\circ} n - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

Divide both sides by

18

18 x = 234 0^{\circ} + 648 0^{\circ} n - 18 arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

Divide both sides by

18

\frac{18 x}{18} = 13 0^{\circ} + \frac{648 0 ^{\circ} n}{18} - \frac{18 arcsin ( \frac{1}{2 s i n ( 4 0 ^{\circ} )} )}{18}

Simplify

\frac{18 x}{18} = 13 0^{\circ} + \frac{648 0 ^{\circ} n}{18} - \frac{18 arcsin ( \frac{1}{2 s i n ( 4 0 ^{\circ} )} )}{18}

Simplify

\frac{18 x}{18} : x

\frac{18 x}{18}

Divide the numbers:

\frac{18}{18} = 1

= x

Simplify

13 0^{\circ} + \frac{648 0 ^{\circ} n}{18} - \frac{18 arcsin ( \frac{1}{2 s i n ( 4 0 ^{\circ} )} )}{18} : 13 0^{\circ} + 36 0^{\circ} n - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

13 0^{\circ} + \frac{648 0 ^{\circ} n}{18} - \frac{18 arcsin ( \frac{1}{2 s i n ( 4 0 ^{\circ} )} )}{18}

Divide the numbers:

\frac{36}{18} = 2

= 13 0^{\circ} + 36 0^{\circ} n - \frac{18 arcsin ( \frac{1}{2 s i n ( 4 0 ^{\circ} )} )}{18}

Divide the numbers:

\frac{18}{18} = 1

= 13 0^{\circ} + 36 0^{\circ} n - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

x = 13 0^{\circ} + 36 0^{\circ} n - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

x = 13 0^{\circ} + 36 0^{\circ} n - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

x = 13 0^{\circ} + 36 0^{\circ} n - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

x = - 5 0^{\circ} + 36 0^{\circ} n + arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )}), x = 13 0^{\circ} + 36 0^{\circ} n - arcsin (\frac{1}{2 sin ( 4 0 ^{\circ} )})

Show solutions in decimal form

x = - 5 0^{\circ} + 36 0^{\circ} n + 0.89125 \dots, x = 13 0^{\circ} + 36 0^{\circ} n - 0.89125 \dots

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Frequently Asked Questions (FAQ)

What is the general solution for cos(x+10)-cos(x+90)=1 ?
The general solution for cos(x+10)-cos(x+90)=1 is x=-50+360n+0.89125…,x=130+360n-0.89125…