1+2cos^2(x)-4sin^2(x)=3cos(2x)

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Solution for 1+2cos^2(x)-4sin^2(x)=3cos(2x) equation: 


Simplifying
1 + 2cos2(x) + -4sin2(x) = 3cos(2x)

Multiply cos2 * x
1 + 2cos2x + -4sin2(x) = 3cos(2x)

Multiply in2s * x
1 + 2cos2x + -4in2sx = 3cos(2x)

Remove parenthesis around (2x)
1 + 2cos2x + -4in2sx = 3cos * 2x

Reorder the terms for easier multiplication:
1 + 2cos2x + -4in2sx = 3 * 2cos * x

Multiply 3 * 2
1 + 2cos2x + -4in2sx = 6cos * x

Multiply cos * x
1 + 2cos2x + -4in2sx = 6cosx

Solving
1 + 2cos2x + -4in2sx = 6cosx

Solving for variable 'c'.

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

Add '-6cosx' to each side of the equation.
1 + 2cos2x + -6cosx + -4in2sx = 6cosx + -6cosx

Reorder the terms:
1 + -6cosx + 2cos2x + -4in2sx = 6cosx + -6cosx

Combine like terms: 6cosx + -6cosx = 0
1 + -6cosx + 2cos2x + -4in2sx = 0

Add '-1' to each side of the equation.
1 + -6cosx + 2cos2x + -1 + -4in2sx = 0 + -1

Reorder the terms:
1 + -1 + -6cosx + 2cos2x + -4in2sx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6cosx + 2cos2x + -4in2sx = 0 + -1
-6cosx + 2cos2x + -4in2sx = 0 + -1

Combine like terms: 0 + -1 = -1
-6cosx + 2cos2x + -4in2sx = -1

Add '4in2sx' to each side of the equation.
-6cosx + 2cos2x + -4in2sx + 4in2sx = -1 + 4in2sx

Combine like terms: -4in2sx + 4in2sx = 0
-6cosx + 2cos2x + 0 = -1 + 4in2sx
-6cosx + 2cos2x = -1 + 4in2sx

Reorder the terms:
1 + -6cosx + 2cos2x + -4in2sx = -1 + 4in2sx + 1 + -4in2sx

Reorder the terms:
1 + -6cosx + 2cos2x + -4in2sx = -1 + 1 + 4in2sx + -4in2sx

Combine like terms: -1 + 1 = 0
1 + -6cosx + 2cos2x + -4in2sx = 0 + 4in2sx + -4in2sx
1 + -6cosx + 2cos2x + -4in2sx = 4in2sx + -4in2sx

Combine like terms: 4in2sx + -4in2sx = 0
1 + -6cosx + 2cos2x + -4in2sx = 0

The solution to this equation could not be determined.

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