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

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


Simplifying
cos4x + -1sin4x = cos(2x)

Remove parenthesis around (2x)
cos4x + -1in4sx = cos * 2x

Reorder the terms for easier multiplication:
cos4x + -1in4sx = 2cos * x

Multiply cos * x
cos4x + -1in4sx = 2cosx

Solving
cos4x + -1in4sx = 2cosx

Solving for variable 'c'.

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

Add '-2cosx' to each side of the equation.
cos4x + -2cosx + -1in4sx = 2cosx + -2cosx

Reorder the terms:
-2cosx + cos4x + -1in4sx = 2cosx + -2cosx

Combine like terms: 2cosx + -2cosx = 0
-2cosx + cos4x + -1in4sx = 0

Add 'in4sx' to each side of the equation.
-2cosx + cos4x + -1in4sx + in4sx = 0 + in4sx

Combine like terms: -1in4sx + in4sx = 0
-2cosx + cos4x + 0 = 0 + in4sx
-2cosx + cos4x = 0 + in4sx
Remove the zero:
-2cosx + cos4x = in4sx

Combine like terms: in4sx + -1in4sx = 0
-2cosx + cos4x + -1in4sx = 0

Factor out the Greatest Common Factor (GCF), 'sx'.
sx(-2co + cos3 + -1in4) = 0


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

Simplifying
sx = 0

Solving
sx = 0

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

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

Simplifying
0 = -1sx

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 '(-2co + cos3 + -1in4)' equal to zero and attempt to solve:

Simplifying
-2co + cos3 + -1in4 = 0

Solving
-2co + cos3 + -1in4 = 0

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

Add 'in4' to each side of the equation.
-2co + cos3 + -1in4 + in4 = 0 + in4

Combine like terms: -1in4 + in4 = 0
-2co + cos3 + 0 = 0 + in4
-2co + cos3 = 0 + in4
Remove the zero:
-2co + cos3 = in4

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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