Cos(x)+cos(5x)=cos(3x)+cos(7x)

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Solution for Cos(x)+cos(5x)=cos(3x)+cos(7x) equation:


Simplifying
Cos(x) + cos(5x) = cos(3x) + cos(7x)

Multiply osC * x
osxC + cos(5x) = cos(3x) + cos(7x)

Remove parenthesis around (5x)
osxC + cos * 5x = cos(3x) + cos(7x)

Reorder the terms for easier multiplication:
osxC + 5cos * x = cos(3x) + cos(7x)

Multiply cos * x
osxC + 5cosx = cos(3x) + cos(7x)

Reorder the terms:
5cosx + osxC = cos(3x) + cos(7x)

Remove parenthesis around (3x)
5cosx + osxC = cos * 3x + cos(7x)

Reorder the terms for easier multiplication:
5cosx + osxC = 3cos * x + cos(7x)

Multiply cos * x
5cosx + osxC = 3cosx + cos(7x)

Remove parenthesis around (7x)
5cosx + osxC = 3cosx + cos * 7x

Reorder the terms for easier multiplication:
5cosx + osxC = 3cosx + 7cos * x

Multiply cos * x
5cosx + osxC = 3cosx + 7cosx

Combine like terms: 3cosx + 7cosx = 10cosx
5cosx + osxC = 10cosx

Solving
5cosx + osxC = 10cosx

Solving for variable 'c'.

Move all terms containing c to the left, all other terms to the right.

Add '-10cosx' to each side of the equation.
5cosx + -10cosx + osxC = 10cosx + -10cosx

Combine like terms: 5cosx + -10cosx = -5cosx
-5cosx + osxC = 10cosx + -10cosx

Combine like terms: 10cosx + -10cosx = 0
-5cosx + osxC = 0

Add '-1osxC' to each side of the equation.
-5cosx + osxC + -1osxC = 0 + -1osxC

Combine like terms: osxC + -1osxC = 0
-5cosx + 0 = 0 + -1osxC
-5cosx = 0 + -1osxC
Remove the zero:
-5cosx = -1osxC

Divide each side by '-5osx'.
c = 0.2C

Simplifying
c = 0.2C

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