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Simplifying cos(x) + cos(3x) = 2sin(6x) * cos(x) Multiply cos * x cosx + cos(3x) = 2sin(6x) * cos(x) Remove parenthesis around (3x) cosx + cos * 3x = 2sin(6x) * cos(x) Reorder the terms for easier multiplication: cosx + 3cos * x = 2sin(6x) * cos(x) Multiply cos * x cosx + 3cosx = 2sin(6x) * cos(x) Combine like terms: cosx + 3cosx = 4cosx 4cosx = 2sin(6x) * cos(x) Remove parenthesis around (6x) 4cosx = 2ins * 6x * cos(x) Reorder the terms for easier multiplication: 4cosx = 2 * 6ins * x * cos * x Multiply 2 * 6 4cosx = 12ins * x * cos * x Multiply ins * x 4cosx = 12insx * cos * x Multiply insx * cos 4cosx = 12cinos2x * x Multiply cinos2x * x 4cosx = 12cinos2x2 Solving 4cosx = 12cinos2x2 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-12cinos2x2' to each side of the equation. -12cinos2x2 + 4cosx = 12cinos2x2 + -12cinos2x2 Combine like terms: 12cinos2x2 + -12cinos2x2 = 0 -12cinos2x2 + 4cosx = 0 Factor out the Greatest Common Factor (GCF), '4cosx'. 4cosx(-3insx + 1) = 0 Ignore the factor 4.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 '(-3insx + 1)' equal to zero and attempt to solve: Simplifying -3insx + 1 = 0 Reorder the terms: 1 + -3insx = 0 Solving 1 + -3insx = 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 + -3insx = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3insx = 0 + -1 -3insx = 0 + -1 Combine like terms: 0 + -1 = -1 -3insx = -1 Add '3insx' to each side of the equation. -3insx + 3insx = -1 + 3insx Combine like terms: -3insx + 3insx = 0 0 = -1 + 3insx Simplifying 0 = -1 + 3insx 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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