cos(x)+cos(2x)+cos(3x)+cos(4x)+cos(5x)=5

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Solution for cos(x)+cos(2x)+cos(3x)+cos(4x)+cos(5x)=5 equation: 


Simplifying
cos(x) + cos(2x) + cos(3x) + cos(4x) + cos(5x) = 5

Multiply cos * x
cosx + cos(2x) + cos(3x) + cos(4x) + cos(5x) = 5

Remove parenthesis around (2x)
cosx + cos * 2x + cos(3x) + cos(4x) + cos(5x) = 5

Reorder the terms for easier multiplication:
cosx + 2cos * x + cos(3x) + cos(4x) + cos(5x) = 5

Multiply cos * x
cosx + 2cosx + cos(3x) + cos(4x) + cos(5x) = 5

Remove parenthesis around (3x)
cosx + 2cosx + cos * 3x + cos(4x) + cos(5x) = 5

Reorder the terms for easier multiplication:
cosx + 2cosx + 3cos * x + cos(4x) + cos(5x) = 5

Multiply cos * x
cosx + 2cosx + 3cosx + cos(4x) + cos(5x) = 5

Remove parenthesis around (4x)
cosx + 2cosx + 3cosx + cos * 4x + cos(5x) = 5

Reorder the terms for easier multiplication:
cosx + 2cosx + 3cosx + 4cos * x + cos(5x) = 5

Multiply cos * x
cosx + 2cosx + 3cosx + 4cosx + cos(5x) = 5

Remove parenthesis around (5x)
cosx + 2cosx + 3cosx + 4cosx + cos * 5x = 5

Reorder the terms for easier multiplication:
cosx + 2cosx + 3cosx + 4cosx + 5cos * x = 5

Multiply cos * x
cosx + 2cosx + 3cosx + 4cosx + 5cosx = 5

Combine like terms: cosx + 2cosx = 3cosx
3cosx + 3cosx + 4cosx + 5cosx = 5

Combine like terms: 3cosx + 3cosx = 6cosx
6cosx + 4cosx + 5cosx = 5

Combine like terms: 6cosx + 4cosx = 10cosx
10cosx + 5cosx = 5

Combine like terms: 10cosx + 5cosx = 15cosx
15cosx = 5

Solving
15cosx = 5

Solving for variable 'c'.

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

Divide each side by '15osx'.
c = 0.3333333333o-1s-1x-1

Simplifying
c = 0.3333333333o-1s-1x-1

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