sin(3x-27)=cos(5x+5)

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Solution for sin(3x-27)=cos(5x+5) equation:


Simplifying
sin(3x + -27) = cos(5x + 5)

Reorder the terms:
ins(-27 + 3x) = cos(5x + 5)
(-27 * ins + 3x * ins) = cos(5x + 5)
(-27ins + 3insx) = cos(5x + 5)

Reorder the terms:
-27ins + 3insx = cos(5 + 5x)
-27ins + 3insx = (5 * cos + 5x * cos)
-27ins + 3insx = (5cos + 5cosx)

Solving
-27ins + 3insx = 5cos + 5cosx

Solving for variable 'i'.

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

Reorder the terms:
-5cos + -5cosx + -27ins + 3insx = 5cos + 5cosx + -5cos + -5cosx

Reorder the terms:
-5cos + -5cosx + -27ins + 3insx = 5cos + -5cos + 5cosx + -5cosx

Combine like terms: 5cos + -5cos = 0
-5cos + -5cosx + -27ins + 3insx = 0 + 5cosx + -5cosx
-5cos + -5cosx + -27ins + 3insx = 5cosx + -5cosx

Combine like terms: 5cosx + -5cosx = 0
-5cos + -5cosx + -27ins + 3insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-5co + -5cox + -27in + 3inx) = 0

Subproblem 1

Set the factor 's' equal to zero and attempt to solve: Simplifying s = 0 Solving s = 0 Move all terms containing i 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 + -5cox + -27in + 3inx)' equal to zero and attempt to solve: Simplifying -5co + -5cox + -27in + 3inx = 0 Solving -5co + -5cox + -27in + 3inx = 0 Move all terms containing i to the left, all other terms to the right. Add '5co' to each side of the equation. -5co + -5cox + -27in + 5co + 3inx = 0 + 5co Reorder the terms: -5co + 5co + -5cox + -27in + 3inx = 0 + 5co Combine like terms: -5co + 5co = 0 0 + -5cox + -27in + 3inx = 0 + 5co -5cox + -27in + 3inx = 0 + 5co Remove the zero: -5cox + -27in + 3inx = 5co Add '5cox' to each side of the equation. -5cox + -27in + 5cox + 3inx = 5co + 5cox Reorder the terms: -5cox + 5cox + -27in + 3inx = 5co + 5cox Combine like terms: -5cox + 5cox = 0 0 + -27in + 3inx = 5co + 5cox -27in + 3inx = 5co + 5cox 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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