cos(4x-20)=sin(8x-40)

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Solution for cos(4x-20)=sin(8x-40) equation:


Simplifying
cos(4x + -20) = sin(8x + -40)

Reorder the terms:
cos(-20 + 4x) = sin(8x + -40)
(-20 * cos + 4x * cos) = sin(8x + -40)
(-20cos + 4cosx) = sin(8x + -40)

Reorder the terms:
-20cos + 4cosx = ins(-40 + 8x)
-20cos + 4cosx = (-40 * ins + 8x * ins)
-20cos + 4cosx = (-40ins + 8insx)

Solving
-20cos + 4cosx = -40ins + 8insx

Solving for variable 'c'.

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

Reorder the terms:
-20cos + 4cosx + 40ins + -8insx = -40ins + 40ins + 8insx + -8insx

Combine like terms: -40ins + 40ins = 0
-20cos + 4cosx + 40ins + -8insx = 0 + 8insx + -8insx
-20cos + 4cosx + 40ins + -8insx = 8insx + -8insx

Combine like terms: 8insx + -8insx = 0
-20cos + 4cosx + 40ins + -8insx = 0

Factor out the Greatest Common Factor (GCF), '4s'.
4s(-5co + cox + 10in + -2inx) = 0

Ignore the factor 4.

Subproblem 1

Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing c to the left, all other terms to the right. Add '-1s' to each side of the equation. s + -1s = 0 + -1s Remove the zero: 0 = -1s Simplifying 0 = -1s 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 '(-5co + cox + 10in + -2inx)' equal to zero and attempt to solve: Simplifying -5co + cox + 10in + -2inx = 0 Solving -5co + cox + 10in + -2inx = 0 Move all terms containing c to the left, all other terms to the right. Add '-10in' to each side of the equation. -5co + cox + 10in + -10in + -2inx = 0 + -10in Combine like terms: 10in + -10in = 0 -5co + cox + 0 + -2inx = 0 + -10in -5co + cox + -2inx = 0 + -10in Remove the zero: -5co + cox + -2inx = -10in Add '2inx' to each side of the equation. -5co + cox + -2inx + 2inx = -10in + 2inx Combine like terms: -2inx + 2inx = 0 -5co + cox + 0 = -10in + 2inx -5co + cox = -10in + 2inx 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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