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Simplifying cosx = 4cos3x + -3cosx Reorder the terms: cosx = -3cosx + 4cos3x Solving cosx = -3cosx + 4cos3x Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '3cosx' to each side of the equation. cosx + 3cosx = -3cosx + 3cosx + 4cos3x Combine like terms: cosx + 3cosx = 4cosx 4cosx = -3cosx + 3cosx + 4cos3x Combine like terms: -3cosx + 3cosx = 0 4cosx = 0 + 4cos3x 4cosx = 4cos3x Add '-4cos3x' to each side of the equation. 4cosx + -4cos3x = 4cos3x + -4cos3x Combine like terms: 4cos3x + -4cos3x = 0 4cosx + -4cos3x = 0 Factor out the Greatest Common Factor (GCF), '4cosx'. 4cosx(1 + -1s2) = 0 Factor a difference between two squares. 4cosx((1 + s)(1 + -1s)) = 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 '(1 + s)' equal to zero and attempt to solve: Simplifying 1 + s = 0 Solving 1 + s = 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 + s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + s = 0 + -1 s = 0 + -1 Combine like terms: 0 + -1 = -1 s = -1 Add '-1s' to each side of the equation. s + -1s = -1 + -1s Combine like terms: s + -1s = 0 0 = -1 + -1s Simplifying 0 = -1 + -1s The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + -1s)' equal to zero and attempt to solve: Simplifying 1 + -1s = 0 Solving 1 + -1s = 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 + -1s = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1s = 0 + -1 -1s = 0 + -1 Combine like terms: 0 + -1 = -1 -1s = -1 Add 's' to each side of the equation. -1s + s = -1 + s Combine like terms: -1s + s = 0 0 = -1 + s Simplifying 0 = -1 + s 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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