sin(2x)sin(x)-cos(2x)cos(x)=-cos(x)

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Solution for sin(2x)sin(x)-cos(2x)cos(x)=-cos(x) equation:


Simplifying
sin(2x) * sin(x) + -1cos(2x) * cos(x) = -1cos(x)

Remove parenthesis around (2x)
ins * 2x * sin(x) + -1cos(2x) * cos(x) = -1cos(x)

Reorder the terms for easier multiplication:
2ins * x * ins * x + -1cos(2x) * cos(x) = -1cos(x)

Multiply ins * x
2insx * ins * x + -1cos(2x) * cos(x) = -1cos(x)

Multiply insx * ins
2i2n2s2x * x + -1cos(2x) * cos(x) = -1cos(x)

Multiply i2n2s2x * x
2i2n2s2x2 + -1cos(2x) * cos(x) = -1cos(x)

Remove parenthesis around (2x)
2i2n2s2x2 + -1cos * 2x * cos(x) = -1cos(x)

Reorder the terms for easier multiplication:
2i2n2s2x2 + -1 * 2cos * x * cos * x = -1cos(x)

Multiply -1 * 2
2i2n2s2x2 + -2cos * x * cos * x = -1cos(x)

Multiply cos * x
2i2n2s2x2 + -2cosx * cos * x = -1cos(x)

Multiply cosx * cos
2i2n2s2x2 + -2c2o2s2x * x = -1cos(x)

Multiply c2o2s2x * x
2i2n2s2x2 + -2c2o2s2x2 = -1cos(x)

Reorder the terms:
-2c2o2s2x2 + 2i2n2s2x2 = -1cos(x)

Multiply cos * x
-2c2o2s2x2 + 2i2n2s2x2 = -1cosx

Solving
-2c2o2s2x2 + 2i2n2s2x2 = -1cosx

Solving for variable 'c'.

Reorder the terms:
cosx + -2c2o2s2x2 + 2i2n2s2x2 = -1cosx + cosx

Combine like terms: -1cosx + cosx = 0
cosx + -2c2o2s2x2 + 2i2n2s2x2 = 0

Factor out the Greatest Common Factor (GCF), 'sx'.
sx(co + -2c2o2sx + 2i2n2sx) = 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 + -2c2o2sx + 2i2n2sx)' equal to zero and attempt to solve: Simplifying co + -2c2o2sx + 2i2n2sx = 0 Solving co + -2c2o2sx + 2i2n2sx = 0 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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