Cos(3x)=cos(5x)

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


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

Remove parenthesis around (3x)
osC * 3x = cos(5x)

Reorder the terms for easier multiplication:
3osC * x = cos(5x)

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

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

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

Multiply cos * x
3osxC = 5cosx

Solving
3osxC = 5cosx

Solving for variable 'o'.

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

Add '-5cosx' to each side of the equation.
-5cosx + 3osxC = 5cosx + -5cosx

Combine like terms: 5cosx + -5cosx = 0
-5cosx + 3osxC = 0

Factor out the Greatest Common Factor (GCF), 'osx'.
osx(-5c + 3C) = 0

Subproblem 1

Set the factor 'osx' equal to zero and attempt to solve: Simplifying osx = 0 Solving osx = 0 Move all terms containing o to the left, all other terms to the right. Simplifying osx = 0 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 '(-5c + 3C)' equal to zero and attempt to solve: Simplifying -5c + 3C = 0 Reorder the terms: 3C + -5c = 0 Solving 3C + -5c = 0 Move all terms containing o to the left, all other terms to the right. Add '-3C' to each side of the equation. 3C + -3C + -5c = 0 + -3C Combine like terms: 3C + -3C = 0 0 + -5c = 0 + -3C -5c = 0 + -3C Remove the zero: -5c = -3C Add '5c' to each side of the equation. -5c + 5c = -3C + 5c Combine like terms: -5c + 5c = 0 0 = -3C + 5c Simplifying 0 = -3C + 5c 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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