Cos(x+60)-cos(x-120)=cosx

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Solution for Cos(x+60)-cos(x-120)=cosx equation:


Simplifying
Cos(x + 60) + -1cos(x + -120) = cosx

Reorder the terms:
osC(60 + x) + -1cos(x + -120) = cosx
(60 * osC + x * osC) + -1cos(x + -120) = cosx
(60osC + osxC) + -1cos(x + -120) = cosx

Reorder the terms:
60osC + osxC + -1cos(-120 + x) = cosx
60osC + osxC + (-120 * -1cos + x * -1cos) = cosx
60osC + osxC + (120cos + -1cosx) = cosx

Reorder the terms:
120cos + -1cosx + 60osC + osxC = cosx

Solving
120cos + -1cosx + 60osC + osxC = cosx

Solving for variable 'c'.

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

Add '-1cosx' to each side of the equation.
120cos + -1cosx + 60osC + -1cosx + osxC = cosx + -1cosx

Reorder the terms:
120cos + -1cosx + -1cosx + 60osC + osxC = cosx + -1cosx

Combine like terms: -1cosx + -1cosx = -2cosx
120cos + -2cosx + 60osC + osxC = cosx + -1cosx

Combine like terms: cosx + -1cosx = 0
120cos + -2cosx + 60osC + osxC = 0

Add '-60osC' to each side of the equation.
120cos + -2cosx + 60osC + -60osC + osxC = 0 + -60osC

Combine like terms: 60osC + -60osC = 0
120cos + -2cosx + 0 + osxC = 0 + -60osC
120cos + -2cosx + osxC = 0 + -60osC
Remove the zero:
120cos + -2cosx + osxC = -60osC

Add '-1osxC' to each side of the equation.
120cos + -2cosx + osxC + -1osxC = -60osC + -1osxC

Combine like terms: osxC + -1osxC = 0
120cos + -2cosx + 0 = -60osC + -1osxC
120cos + -2cosx = -60osC + -1osxC

Reorder the terms:
120cos + -2cosx + 60osC + osxC = -60osC + 60osC + -1osxC + osxC

Combine like terms: -60osC + 60osC = 0
120cos + -2cosx + 60osC + osxC = 0 + -1osxC + osxC
120cos + -2cosx + 60osC + osxC = -1osxC + osxC

Combine like terms: -1osxC + osxC = 0
120cos + -2cosx + 60osC + osxC = 0

Factor out the Greatest Common Factor (GCF), 'os'.
os(120c + -2cx + 60C + xC) = 0

Subproblem 1

Set the factor 'os' equal to zero and attempt to solve: Simplifying os = 0 Solving os = 0 Move all terms containing c to the left, all other terms to the right. Add '-1os' to each side of the equation. os + -1os = 0 + -1os Remove the zero: 0 = -1os Simplifying 0 = -1os The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Subproblem 2

Set the factor '(120c + -2cx + 60C + xC)' equal to zero and attempt to solve: Simplifying 120c + -2cx + 60C + xC = 0 Reorder the terms: 60C + 120c + -2cx + xC = 0 Solving 60C + 120c + -2cx + xC = 0 Move all terms containing c to the left, all other terms to the right. Add '-60C' to each side of the equation. 60C + 120c + -2cx + -60C + xC = 0 + -60C Reorder the terms: 60C + -60C + 120c + -2cx + xC = 0 + -60C Combine like terms: 60C + -60C = 0 0 + 120c + -2cx + xC = 0 + -60C 120c + -2cx + xC = 0 + -60C Remove the zero: 120c + -2cx + xC = -60C Add '-1xC' to each side of the equation. 120c + -2cx + xC + -1xC = -60C + -1xC Combine like terms: xC + -1xC = 0 120c + -2cx + 0 = -60C + -1xC 120c + -2cx = -60C + -1xC The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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