2cos^2(x)+cosx-sin^2(x)=0

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Solution for 2cos^2(x)+cosx-sin^2(x)=0 equation: 


Simplifying
2cos2(x) + cosx + -1sin2(x) = 0

Multiply cos2 * x
2cos2x + cosx + -1sin2(x) = 0

Multiply in2s * x
2cos2x + cosx + -1in2sx = 0

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

Solving
cosx + 2cos2x + -1in2sx = 0

Solving for variable 'c'.

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

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

Combine like terms: -1in2sx + in2sx = 0
cosx + 2cos2x + 0 = 0 + in2sx
cosx + 2cos2x = 0 + in2sx
Remove the zero:
cosx + 2cos2x = in2sx

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

Factor out the Greatest Common Factor (GCF), 'sx'.
sx(co + 2cos + -1in2) = 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 '(co + 2cos + -1in2)' equal to zero and attempt to solve:

Simplifying
co + 2cos + -1in2 = 0

Solving
co + 2cos + -1in2 = 0

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

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

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