2cos(x)=-2cost(2x)

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


Simplifying
2cos(x) = -2cost(2x)

Multiply cos * x
2cosx = -2cost(2x)

Remove parenthesis around (2x)
2cosx = -2cost * 2x

Reorder the terms for easier multiplication:
2cosx = -2 * 2cost * x

Multiply -2 * 2
2cosx = -4cost * x

Multiply cost * x
2cosx = -4costx

Solving
2cosx = -4costx

Solving for variable 'c'.

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

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

Combine like terms: -4costx + 4costx = 0
4costx + 2cosx = 0

Factor out the Greatest Common Factor (GCF), '2cosx'.
2cosx(2t + 1) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'cosx' equal to zero and attempt to solve: Simplifying cosx = 0 Solving cosx = 0 Move all terms containing c to the left, all other terms to the right. Simplifying cosx = 0 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 '(2t + 1)' equal to zero and attempt to solve: Simplifying 2t + 1 = 0 Reorder the terms: 1 + 2t = 0 Solving 1 + 2t = 0 Move all terms containing c to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2t = 0 + -1 2t = 0 + -1 Combine like terms: 0 + -1 = -1 2t = -1 Add '-2t' to each side of the equation. 2t + -2t = -1 + -2t Combine like terms: 2t + -2t = 0 0 = -1 + -2t Simplifying 0 = -1 + -2t 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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