cos(x)-cos(2x)+cos(3x)-cos(4x)=0.5

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Solution for cos(x)-cos(2x)+cos(3x)-cos(4x)=0.5 equation:


Simplifying
cos(x) + -1cos(2x) + cos(3x) + -1cos(4x) = 0.5

Multiply cos * x
cosx + -1cos(2x) + cos(3x) + -1cos(4x) = 0.5

Remove parenthesis around (2x)
cosx + -1cos * 2x + cos(3x) + -1cos(4x) = 0.5

Reorder the terms for easier multiplication:
cosx + -1 * 2cos * x + cos(3x) + -1cos(4x) = 0.5

Multiply -1 * 2
cosx + -2cos * x + cos(3x) + -1cos(4x) = 0.5

Multiply cos * x
cosx + -2cosx + cos(3x) + -1cos(4x) = 0.5

Remove parenthesis around (3x)
cosx + -2cosx + cos * 3x + -1cos(4x) = 0.5

Reorder the terms for easier multiplication:
cosx + -2cosx + 3cos * x + -1cos(4x) = 0.5

Multiply cos * x
cosx + -2cosx + 3cosx + -1cos(4x) = 0.5

Remove parenthesis around (4x)
cosx + -2cosx + 3cosx + -1cos * 4x = 0.5

Reorder the terms for easier multiplication:
cosx + -2cosx + 3cosx + -1 * 4cos * x = 0.5

Multiply -1 * 4
cosx + -2cosx + 3cosx + -4cos * x = 0.5

Multiply cos * x
cosx + -2cosx + 3cosx + -4cosx = 0.5

Combine like terms: cosx + -2cosx = -1cosx
-1cosx + 3cosx + -4cosx = 0.5

Combine like terms: -1cosx + 3cosx = 2cosx
2cosx + -4cosx = 0.5

Combine like terms: 2cosx + -4cosx = -2cosx
-2cosx = 0.5

Solving
-2cosx = 0.5

Solving for variable 'c'.

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

Divide each side by '-2osx'.
c = -0.25o-1s-1x-1

Simplifying
c = -0.25o-1s-1x-1

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