cosine^2(4x)-sine^2(4x)=cosine(x)

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


Simplifying
cosine2(4x) + -1sine2(4x) = cosine(x)

Remove parenthesis around (4x)
ce2inos * 4x + -1sine2(4x) = cosine(x)

Reorder the terms for easier multiplication:
4ce2inos * x + -1sine2(4x) = cosine(x)

Multiply ce2inos * x
4ce2inosx + -1sine2(4x) = cosine(x)

Remove parenthesis around (4x)
4ce2inosx + -1e2ins * 4x = cosine(x)

Reorder the terms for easier multiplication:
4ce2inosx + -1 * 4e2ins * x = cosine(x)

Multiply -1 * 4
4ce2inosx + -4e2ins * x = cosine(x)

Multiply e2ins * x
4ce2inosx + -4e2insx = cosine(x)

Multiply ceinos * x
4ce2inosx + -4e2insx = ceinosx

Solving
4ce2inosx + -4e2insx = ceinosx

Solving for variable 'c'.

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

Add '-1ceinosx' to each side of the equation.
4ce2inosx + -1ceinosx + -4e2insx = ceinosx + -1ceinosx

Reorder the terms:
-1ceinosx + 4ce2inosx + -4e2insx = ceinosx + -1ceinosx

Combine like terms: ceinosx + -1ceinosx = 0
-1ceinosx + 4ce2inosx + -4e2insx = 0

Add '4e2insx' to each side of the equation.
-1ceinosx + 4ce2inosx + -4e2insx + 4e2insx = 0 + 4e2insx

Combine like terms: -4e2insx + 4e2insx = 0
-1ceinosx + 4ce2inosx + 0 = 0 + 4e2insx
-1ceinosx + 4ce2inosx = 0 + 4e2insx
Remove the zero:
-1ceinosx + 4ce2inosx = 4e2insx

Combine like terms: 4e2insx + -4e2insx = 0
-1ceinosx + 4ce2inosx + -4e2insx = 0

Factor out the Greatest Common Factor (GCF), 'einsx'.
einsx(-1co + 4ceo + -4e) = 0


Subproblem 1
Set the factor 'einsx' equal to zero and attempt to solve:

Simplifying
einsx = 0

Solving
einsx = 0

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

Add '-1einsx' to each side of the equation.
einsx + -1einsx = 0 + -1einsx
Remove the zero:
0 = -1einsx

Simplifying
0 = -1einsx

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 '(-1co + 4ceo + -4e)' equal to zero and attempt to solve:

Simplifying
-1co + 4ceo + -4e = 0

Reorder the terms:
4ceo + -1co + -4e = 0

Solving
4ceo + -1co + -4e = 0

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

Add '4e' to each side of the equation.
4ceo + -1co + -4e + 4e = 0 + 4e

Combine like terms: -4e + 4e = 0
4ceo + -1co + 0 = 0 + 4e
4ceo + -1co = 0 + 4e
Remove the zero:
4ceo + -1co = 4e

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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