cos(4x+15)=cos(2x-15)

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Solution for cos(4x+15)=cos(2x-15) equation:


Simplifying
cos(4x + 15) = cos(2x + -15)

Reorder the terms:
cos(15 + 4x) = cos(2x + -15)
(15 * cos + 4x * cos) = cos(2x + -15)
(15cos + 4cosx) = cos(2x + -15)

Reorder the terms:
15cos + 4cosx = cos(-15 + 2x)
15cos + 4cosx = (-15 * cos + 2x * cos)
15cos + 4cosx = (-15cos + 2cosx)

Solving
15cos + 4cosx = -15cos + 2cosx

Solving for variable 'c'.

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

Add '15cos' to each side of the equation.
15cos + 15cos + 4cosx = -15cos + 15cos + 2cosx

Combine like terms: 15cos + 15cos = 30cos
30cos + 4cosx = -15cos + 15cos + 2cosx

Combine like terms: -15cos + 15cos = 0
30cos + 4cosx = 0 + 2cosx
30cos + 4cosx = 2cosx

Add '-2cosx' to each side of the equation.
30cos + 4cosx + -2cosx = 2cosx + -2cosx

Combine like terms: 4cosx + -2cosx = 2cosx
30cos + 2cosx = 2cosx + -2cosx

Combine like terms: 2cosx + -2cosx = 0
30cos + 2cosx = 0

Factor out the Greatest Common Factor (GCF), '2cos'.
2cos(15 + x) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'cos' equal to zero and attempt to solve: Simplifying cos = 0 Solving cos = 0 Move all terms containing c to the left, all other terms to the right. Simplifying cos = 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 '(15 + x)' equal to zero and attempt to solve: Simplifying 15 + x = 0 Solving 15 + x = 0 Move all terms containing c to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 0 + -15 Combine like terms: 15 + -15 = 0 0 + x = 0 + -15 x = 0 + -15 Combine like terms: 0 + -15 = -15 x = -15 Add '-1x' to each side of the equation. x + -1x = -15 + -1x Combine like terms: x + -1x = 0 0 = -15 + -1x Simplifying 0 = -15 + -1x 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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