Cos^4x-sin^4x=cos^2x-sin^2x

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


Simplifying
Cos4x + -1sin4x = cos2x + -1sin2x

Reorder the terms:
-1in4sx + os4xC = cos2x + -1sin2x

Solving
-1in4sx + os4xC = cos2x + -1in2sx

Solving for variable 'i'.

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

Add 'in2sx' to each side of the equation.
-1in4sx + in2sx + os4xC = cos2x + -1in2sx + in2sx

Reorder the terms:
in2sx + -1in4sx + os4xC = cos2x + -1in2sx + in2sx

Combine like terms: -1in2sx + in2sx = 0
in2sx + -1in4sx + os4xC = cos2x + 0
in2sx + -1in4sx + os4xC = cos2x

Add '-1os4xC' to each side of the equation.
in2sx + -1in4sx + os4xC + -1os4xC = cos2x + -1os4xC

Combine like terms: os4xC + -1os4xC = 0
in2sx + -1in4sx + 0 = cos2x + -1os4xC
in2sx + -1in4sx = cos2x + -1os4xC

Reorder the terms:
-1cos2x + in2sx + -1in4sx + os4xC = cos2x + -1os4xC + -1cos2x + os4xC

Reorder the terms:
-1cos2x + in2sx + -1in4sx + os4xC = cos2x + -1cos2x + -1os4xC + os4xC

Combine like terms: cos2x + -1cos2x = 0
-1cos2x + in2sx + -1in4sx + os4xC = 0 + -1os4xC + os4xC
-1cos2x + in2sx + -1in4sx + os4xC = -1os4xC + os4xC

Combine like terms: -1os4xC + os4xC = 0
-1cos2x + in2sx + -1in4sx + os4xC = 0

Factor out the Greatest Common Factor (GCF), 'sx'.
sx(-1cos + in2 + -1in4 + os3C) = 0


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

Simplifying
sx = 0

Solving
sx = 0

Move all terms containing i 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 '(-1cos + in2 + -1in4 + os3C)' equal to zero and attempt to solve:

Simplifying
-1cos + in2 + -1in4 + os3C = 0

Solving
-1cos + in2 + -1in4 + os3C = 0

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

Add 'cos' to each side of the equation.
-1cos + in2 + -1in4 + cos + os3C = 0 + cos

Reorder the terms:
-1cos + cos + in2 + -1in4 + os3C = 0 + cos

Combine like terms: -1cos + cos = 0
0 + in2 + -1in4 + os3C = 0 + cos
in2 + -1in4 + os3C = 0 + cos
Remove the zero:
in2 + -1in4 + os3C = cos

Add '-1os3C' to each side of the equation.
in2 + -1in4 + os3C + -1os3C = cos + -1os3C

Combine like terms: os3C + -1os3C = 0
in2 + -1in4 + 0 = cos + -1os3C
in2 + -1in4 = cos + -1os3C

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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