cos^4-sin^4=cos^2-sin^2

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


Simplifying
cos4 + -1sin4 = cos2 + -1sin2

Solving
cos4 + -1in4s = cos2 + -1in2s

Solving for variable 'c'.

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

Add '-1cos2' to each side of the equation.
cos4 + -1cos2 + -1in4s = cos2 + -1cos2 + -1in2s

Reorder the terms:
-1cos2 + cos4 + -1in4s = cos2 + -1cos2 + -1in2s

Combine like terms: cos2 + -1cos2 = 0
-1cos2 + cos4 + -1in4s = 0 + -1in2s
-1cos2 + cos4 + -1in4s = -1in2s

Add 'in4s' to each side of the equation.
-1cos2 + cos4 + -1in4s + in4s = -1in2s + in4s

Combine like terms: -1in4s + in4s = 0
-1cos2 + cos4 + 0 = -1in2s + in4s
-1cos2 + cos4 = -1in2s + in4s

Reorder the terms:
-1cos2 + cos4 + in2s + -1in4s = -1in2s + in2s + in4s + -1in4s

Combine like terms: -1in2s + in2s = 0
-1cos2 + cos4 + in2s + -1in4s = 0 + in4s + -1in4s
-1cos2 + cos4 + in2s + -1in4s = in4s + -1in4s

Combine like terms: in4s + -1in4s = 0
-1cos2 + cos4 + in2s + -1in4s = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-1cos + cos3 + in2 + -1in4) = 0


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

Simplifying
s = 0

Solving
s = 0

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

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

Simplifying
0 = -1s

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 + cos3 + in2 + -1in4)' equal to zero and attempt to solve:

Simplifying
-1cos + cos3 + in2 + -1in4 = 0

Solving
-1cos + cos3 + in2 + -1in4 = 0

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

Add '-1in2' to each side of the equation.
-1cos + cos3 + in2 + -1in2 + -1in4 = 0 + -1in2

Combine like terms: in2 + -1in2 = 0
-1cos + cos3 + 0 + -1in4 = 0 + -1in2
-1cos + cos3 + -1in4 = 0 + -1in2
Remove the zero:
-1cos + cos3 + -1in4 = -1in2

Add 'in4' to each side of the equation.
-1cos + cos3 + -1in4 + in4 = -1in2 + in4

Combine like terms: -1in4 + in4 = 0
-1cos + cos3 + 0 = -1in2 + in4
-1cos + cos3 = -1in2 + 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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