cos^2(5x)+sin^2(5x)=cos(f(x))

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Solution for cos^2(5x)+sin^2(5x)=cos(f(x)) equation: 


Simplifying
cos2(5x) + sin2(5x) = cos(f(x))

Remove parenthesis around (5x)
cos2 * 5x + sin2(5x) = cos(f(x))

Reorder the terms for easier multiplication:
5cos2 * x + sin2(5x) = cos(f(x))

Multiply cos2 * x
5cos2x + sin2(5x) = cos(f(x))

Remove parenthesis around (5x)
5cos2x + in2s * 5x = cos(f(x))

Reorder the terms for easier multiplication:
5cos2x + 5in2s * x = cos(f(x))

Multiply in2s * x
5cos2x + 5in2sx = cos(f(x))

Multiply f * x
5cos2x + 5in2sx = cos(fx)

Multiply cos * fx
5cos2x + 5in2sx = cfosx

Solving
5cos2x + 5in2sx = cfosx

Solving for variable 'c'.

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

Add '-1cfosx' to each side of the equation.
5cos2x + -1cfosx + 5in2sx = cfosx + -1cfosx

Reorder the terms:
-1cfosx + 5cos2x + 5in2sx = cfosx + -1cfosx

Combine like terms: cfosx + -1cfosx = 0
-1cfosx + 5cos2x + 5in2sx = 0

Add '-5in2sx' to each side of the equation.
-1cfosx + 5cos2x + 5in2sx + -5in2sx = 0 + -5in2sx

Combine like terms: 5in2sx + -5in2sx = 0
-1cfosx + 5cos2x + 0 = 0 + -5in2sx
-1cfosx + 5cos2x = 0 + -5in2sx
Remove the zero:
-1cfosx + 5cos2x = -5in2sx

Combine like terms: -5in2sx + 5in2sx = 0
-1cfosx + 5cos2x + 5in2sx = 0

Factor out the Greatest Common Factor (GCF), 'sx'.
sx(-1cfo + 5cos + 5in2) = 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 '(-1cfo + 5cos + 5in2)' equal to zero and attempt to solve:

Simplifying
-1cfo + 5cos + 5in2 = 0

Solving
-1cfo + 5cos + 5in2 = 0

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

Add '-5in2' to each side of the equation.
-1cfo + 5cos + 5in2 + -5in2 = 0 + -5in2

Combine like terms: 5in2 + -5in2 = 0
-1cfo + 5cos + 0 = 0 + -5in2
-1cfo + 5cos = 0 + -5in2
Remove the zero:
-1cfo + 5cos = -5in2

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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