2(sinx-1)(2cos^2x-1)=0

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Solution for 2(sinx-1)(2cos^2x-1)=0 equation:


Simplifying
2(sinx + -1)(2cos2x + -1) = 0

Reorder the terms:
2(-1 + insx)(2cos2x + -1) = 0

Reorder the terms:
2(-1 + insx)(-1 + 2cos2x) = 0

Multiply (-1 + insx) * (-1 + 2cos2x)
2(-1(-1 + 2cos2x) + insx(-1 + 2cos2x)) = 0
2((-1 * -1 + 2cos2x * -1) + insx(-1 + 2cos2x)) = 0
2((1 + -2cos2x) + insx(-1 + 2cos2x)) = 0
2(1 + -2cos2x + (-1 * insx + 2cos2x * insx)) = 0

Reorder the terms:
2(1 + -2cos2x + (2cinos3x2 + -1insx)) = 0
2(1 + -2cos2x + (2cinos3x2 + -1insx)) = 0

Reorder the terms:
2(1 + 2cinos3x2 + -2cos2x + -1insx) = 0
2(1 + 2cinos3x2 + -2cos2x + -1insx) = 0
(1 * 2 + 2cinos3x2 * 2 + -2cos2x * 2 + -1insx * 2) = 0
(2 + 4cinos3x2 + -4cos2x + -2insx) = 0

Solving
2 + 4cinos3x2 + -4cos2x + -2insx = 0

Solving for variable 'c'.

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

Add '-2' to each side of the equation.
2 + 4cinos3x2 + -4cos2x + -2 + -2insx = 0 + -2

Reorder the terms:
2 + -2 + 4cinos3x2 + -4cos2x + -2insx = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 4cinos3x2 + -4cos2x + -2insx = 0 + -2
4cinos3x2 + -4cos2x + -2insx = 0 + -2

Combine like terms: 0 + -2 = -2
4cinos3x2 + -4cos2x + -2insx = -2

Add '2insx' to each side of the equation.
4cinos3x2 + -4cos2x + -2insx + 2insx = -2 + 2insx

Combine like terms: -2insx + 2insx = 0
4cinos3x2 + -4cos2x + 0 = -2 + 2insx
4cinos3x2 + -4cos2x = -2 + 2insx

Reorder the terms:
2 + 4cinos3x2 + -4cos2x + -2insx = -2 + 2insx + 2 + -2insx

Reorder the terms:
2 + 4cinos3x2 + -4cos2x + -2insx = -2 + 2 + 2insx + -2insx

Combine like terms: -2 + 2 = 0
2 + 4cinos3x2 + -4cos2x + -2insx = 0 + 2insx + -2insx
2 + 4cinos3x2 + -4cos2x + -2insx = 2insx + -2insx

Combine like terms: 2insx + -2insx = 0
2 + 4cinos3x2 + -4cos2x + -2insx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 2cinos3x2 + -2cos2x + -1insx) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(1 + 2cinos3x2 + -2cos2x + -1insx)' equal to zero and attempt to solve: Simplifying 1 + 2cinos3x2 + -2cos2x + -1insx = 0 Solving 1 + 2cinos3x2 + -2cos2x + -1insx = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2cinos3x2 + -2cos2x + -1 + -1insx = 0 + -1 Reorder the terms: 1 + -1 + 2cinos3x2 + -2cos2x + -1insx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2cinos3x2 + -2cos2x + -1insx = 0 + -1 2cinos3x2 + -2cos2x + -1insx = 0 + -1 Combine like terms: 0 + -1 = -1 2cinos3x2 + -2cos2x + -1insx = -1 Add 'insx' to each side of the equation. 2cinos3x2 + -2cos2x + -1insx + insx = -1 + insx Combine like terms: -1insx + insx = 0 2cinos3x2 + -2cos2x + 0 = -1 + insx 2cinos3x2 + -2cos2x = -1 + insx 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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