2*sen^2(x)+cos(2x)=4*cos^2(x)

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Solution for 2*sen^2(x)+cos(2x)=4*cos^2(x) equation:


Simplifying
2sen2(x) + cos(2x) = 4cos2(x)

Multiply en2s * x
2en2sx + cos(2x) = 4cos2(x)

Remove parenthesis around (2x)
2en2sx + cos * 2x = 4cos2(x)

Reorder the terms for easier multiplication:
2en2sx + 2cos * x = 4cos2(x)

Multiply cos * x
2en2sx + 2cosx = 4cos2(x)

Reorder the terms:
2cosx + 2en2sx = 4cos2(x)

Multiply cos2 * x
2cosx + 2en2sx = 4cos2x

Solving
2cosx + 2en2sx = 4cos2x

Solving for variable 'c'.

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

Add '-4cos2x' to each side of the equation.
2cosx + -4cos2x + 2en2sx = 4cos2x + -4cos2x

Combine like terms: 4cos2x + -4cos2x = 0
2cosx + -4cos2x + 2en2sx = 0

Add '-2en2sx' to each side of the equation.
2cosx + -4cos2x + 2en2sx + -2en2sx = 0 + -2en2sx

Combine like terms: 2en2sx + -2en2sx = 0
2cosx + -4cos2x + 0 = 0 + -2en2sx
2cosx + -4cos2x = 0 + -2en2sx
Remove the zero:
2cosx + -4cos2x = -2en2sx

Combine like terms: -2en2sx + 2en2sx = 0
2cosx + -4cos2x + 2en2sx = 0

Factor out the Greatest Common Factor (GCF), '2sx'.
2sx(co + -2cos + en2) = 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 '(co + -2cos + en2)' equal to zero and attempt to solve: Simplifying co + -2cos + en2 = 0 Solving co + -2cos + en2 = 0 Move all terms containing c to the left, all other terms to the right. Add '-1en2' to each side of the equation. co + -2cos + en2 + -1en2 = 0 + -1en2 Combine like terms: en2 + -1en2 = 0 co + -2cos + 0 = 0 + -1en2 co + -2cos = 0 + -1en2 Remove the zero: co + -2cos = -1en2 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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