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

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


Simplifying
4cos2(x) + -1sin2(2x) = 4cos4(x)

Multiply cos2 * x
4cos2x + -1sin2(2x) = 4cos4(x)

Remove parenthesis around (2x)
4cos2x + -1in2s * 2x = 4cos4(x)

Reorder the terms for easier multiplication:
4cos2x + -1 * 2in2s * x = 4cos4(x)

Multiply -1 * 2
4cos2x + -2in2s * x = 4cos4(x)

Multiply in2s * x
4cos2x + -2in2sx = 4cos4(x)

Multiply cos4 * x
4cos2x + -2in2sx = 4cos4x

Solving
4cos2x + -2in2sx = 4cos4x

Solving for variable 'c'.

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

Add '-4cos4x' to each side of the equation.
4cos2x + -4cos4x + -2in2sx = 4cos4x + -4cos4x

Combine like terms: 4cos4x + -4cos4x = 0
4cos2x + -4cos4x + -2in2sx = 0

Add '2in2sx' to each side of the equation.
4cos2x + -4cos4x + -2in2sx + 2in2sx = 0 + 2in2sx

Combine like terms: -2in2sx + 2in2sx = 0
4cos2x + -4cos4x + 0 = 0 + 2in2sx
4cos2x + -4cos4x = 0 + 2in2sx
Remove the zero:
4cos2x + -4cos4x = 2in2sx

Combine like terms: 2in2sx + -2in2sx = 0
4cos2x + -4cos4x + -2in2sx = 0

Factor out the Greatest Common Factor (GCF), '2sx'.
2sx(2cos + -2cos3 + -1in2) = 0

Ignore the factor 2.

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 '(2cos + -2cos3 + -1in2)' equal to zero and attempt to solve:

Simplifying
2cos + -2cos3 + -1in2 = 0

Solving
2cos + -2cos3 + -1in2 = 0

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

Add 'in2' to each side of the equation.
2cos + -2cos3 + -1in2 + in2 = 0 + in2

Combine like terms: -1in2 + in2 = 0
2cos + -2cos3 + 0 = 0 + in2
2cos + -2cos3 = 0 + in2
Remove the zero:
2cos + -2cos3 = in2

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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