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Simplifying cos(3x + 10) = cos(5x + -40) Reorder the terms: cos(10 + 3x) = cos(5x + -40) (10 * cos + 3x * cos) = cos(5x + -40) (10cos + 3cosx) = cos(5x + -40) Reorder the terms: 10cos + 3cosx = cos(-40 + 5x) 10cos + 3cosx = (-40 * cos + 5x * cos) 10cos + 3cosx = (-40cos + 5cosx) Solving 10cos + 3cosx = -40cos + 5cosx Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '40cos' to each side of the equation. 10cos + 40cos + 3cosx = -40cos + 40cos + 5cosx Combine like terms: 10cos + 40cos = 50cos 50cos + 3cosx = -40cos + 40cos + 5cosx Combine like terms: -40cos + 40cos = 0 50cos + 3cosx = 0 + 5cosx 50cos + 3cosx = 5cosx Add '-5cosx' to each side of the equation. 50cos + 3cosx + -5cosx = 5cosx + -5cosx Combine like terms: 3cosx + -5cosx = -2cosx 50cos + -2cosx = 5cosx + -5cosx Combine like terms: 5cosx + -5cosx = 0 50cos + -2cosx = 0 Factor out the Greatest Common Factor (GCF), '2cos'. 2cos(25 + -1x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'cos' equal to zero and attempt to solve: Simplifying cos = 0 Solving cos = 0 Move all terms containing c to the left, all other terms to the right. Simplifying cos = 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 '(25 + -1x)' equal to zero and attempt to solve: Simplifying 25 + -1x = 0 Solving 25 + -1x = 0 Move all terms containing c to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -1x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1x = 0 + -25 -1x = 0 + -25 Combine like terms: 0 + -25 = -25 -1x = -25 Add 'x' to each side of the equation. -1x + x = -25 + x Combine like terms: -1x + x = 0 0 = -25 + x Simplifying 0 = -25 + x 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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