sin^2(5x-4)+cos^2(5x-4)=1

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Solution for sin^2(5x-4)+cos^2(5x-4)=1 equation: 


Simplifying
sin2(5x + -4) + cos2(5x + -4) = 1

Reorder the terms:
in2s(-4 + 5x) + cos2(5x + -4) = 1
(-4 * in2s + 5x * in2s) + cos2(5x + -4) = 1
(-4in2s + 5in2sx) + cos2(5x + -4) = 1

Reorder the terms:
-4in2s + 5in2sx + cos2(-4 + 5x) = 1
-4in2s + 5in2sx + (-4 * cos2 + 5x * cos2) = 1
-4in2s + 5in2sx + (-4cos2 + 5cos2x) = 1

Reorder the terms:
-4cos2 + 5cos2x + -4in2s + 5in2sx = 1

Solving
-4cos2 + 5cos2x + -4in2s + 5in2sx = 1

Solving for variable 'c'.

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

Add '4in2s' to each side of the equation.
-4cos2 + 5cos2x + -4in2s + 4in2s + 5in2sx = 1 + 4in2s

Combine like terms: -4in2s + 4in2s = 0
-4cos2 + 5cos2x + 0 + 5in2sx = 1 + 4in2s
-4cos2 + 5cos2x + 5in2sx = 1 + 4in2s

Add '-5in2sx' to each side of the equation.
-4cos2 + 5cos2x + 5in2sx + -5in2sx = 1 + 4in2s + -5in2sx

Combine like terms: 5in2sx + -5in2sx = 0
-4cos2 + 5cos2x + 0 = 1 + 4in2s + -5in2sx
-4cos2 + 5cos2x = 1 + 4in2s + -5in2sx

Reorder the terms:
-1 + -4cos2 + 5cos2x + -4in2s + 5in2sx = 1 + 4in2s + -5in2sx + -1 + -4in2s + 5in2sx

Reorder the terms:
-1 + -4cos2 + 5cos2x + -4in2s + 5in2sx = 1 + -1 + 4in2s + -4in2s + -5in2sx + 5in2sx

Combine like terms: 1 + -1 = 0
-1 + -4cos2 + 5cos2x + -4in2s + 5in2sx = 0 + 4in2s + -4in2s + -5in2sx + 5in2sx
-1 + -4cos2 + 5cos2x + -4in2s + 5in2sx = 4in2s + -4in2s + -5in2sx + 5in2sx

Combine like terms: 4in2s + -4in2s = 0
-1 + -4cos2 + 5cos2x + -4in2s + 5in2sx = 0 + -5in2sx + 5in2sx
-1 + -4cos2 + 5cos2x + -4in2s + 5in2sx = -5in2sx + 5in2sx

Combine like terms: -5in2sx + 5in2sx = 0
-1 + -4cos2 + 5cos2x + -4in2s + 5in2sx = 0

The solution to this equation could not be determined.

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