4cos(4x)=cos^2(2x)-4

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


Simplifying
4cos(4x) = cos2(2x) + -4

Remove parenthesis around (4x)
4cos * 4x = cos2(2x) + -4

Reorder the terms for easier multiplication:
4 * 4cos * x = cos2(2x) + -4

Multiply 4 * 4
16cos * x = cos2(2x) + -4

Multiply cos * x
16cosx = cos2(2x) + -4

Remove parenthesis around (2x)
16cosx = cos2 * 2x + -4

Reorder the terms for easier multiplication:
16cosx = 2cos2 * x + -4

Multiply cos2 * x
16cosx = 2cos2x + -4

Reorder the terms:
16cosx = -4 + 2cos2x

Solving
16cosx = -4 + 2cos2x

Solving for variable 'c'.

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

Add '-2cos2x' to each side of the equation.
16cosx + -2cos2x = -4 + 2cos2x + -2cos2x

Combine like terms: 2cos2x + -2cos2x = 0
16cosx + -2cos2x = -4 + 0
16cosx + -2cos2x = -4

Reorder the terms:
4 + 16cosx + -2cos2x = -4 + 4

Combine like terms: -4 + 4 = 0
4 + 16cosx + -2cos2x = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 8cosx + -1cos2x) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(2 + 8cosx + -1cos2x)' equal to zero and attempt to solve:

Simplifying
2 + 8cosx + -1cos2x = 0

Solving
2 + 8cosx + -1cos2x = 0

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

Add '-2' to each side of the equation.
2 + 8cosx + -2 + -1cos2x = 0 + -2

Reorder the terms:
2 + -2 + 8cosx + -1cos2x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 8cosx + -1cos2x = 0 + -2
8cosx + -1cos2x = 0 + -2

Combine like terms: 0 + -2 = -2
8cosx + -1cos2x = -2

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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