cos(3x+10)=cos(5x-40)

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Solution for cos(3x+10)=cos(5x-40) equation:


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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