sin(2x+2)=cos(3x+8)

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Solution for sin(2x+2)=cos(3x+8) equation:


Simplifying
sin(2x + 2) = cos(3x + 8)

Reorder the terms:
ins(2 + 2x) = cos(3x + 8)
(2 * ins + 2x * ins) = cos(3x + 8)
(2ins + 2insx) = cos(3x + 8)

Reorder the terms:
2ins + 2insx = cos(8 + 3x)
2ins + 2insx = (8 * cos + 3x * cos)
2ins + 2insx = (8cos + 3cosx)

Solving
2ins + 2insx = 8cos + 3cosx

Solving for variable 'i'.

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

Reorder the terms:
-8cos + -3cosx + 2ins + 2insx = 8cos + 3cosx + -8cos + -3cosx

Reorder the terms:
-8cos + -3cosx + 2ins + 2insx = 8cos + -8cos + 3cosx + -3cosx

Combine like terms: 8cos + -8cos = 0
-8cos + -3cosx + 2ins + 2insx = 0 + 3cosx + -3cosx
-8cos + -3cosx + 2ins + 2insx = 3cosx + -3cosx

Combine like terms: 3cosx + -3cosx = 0
-8cos + -3cosx + 2ins + 2insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-8co + -3cox + 2in + 2inx) = 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 '(-8co + -3cox + 2in + 2inx)' equal to zero and attempt to solve: Simplifying -8co + -3cox + 2in + 2inx = 0 Solving -8co + -3cox + 2in + 2inx = 0 Move all terms containing i to the left, all other terms to the right. Add '8co' to each side of the equation. -8co + -3cox + 2in + 8co + 2inx = 0 + 8co Reorder the terms: -8co + 8co + -3cox + 2in + 2inx = 0 + 8co Combine like terms: -8co + 8co = 0 0 + -3cox + 2in + 2inx = 0 + 8co -3cox + 2in + 2inx = 0 + 8co Remove the zero: -3cox + 2in + 2inx = 8co Add '3cox' to each side of the equation. -3cox + 2in + 3cox + 2inx = 8co + 3cox Reorder the terms: -3cox + 3cox + 2in + 2inx = 8co + 3cox Combine like terms: -3cox + 3cox = 0 0 + 2in + 2inx = 8co + 3cox 2in + 2inx = 8co + 3cox 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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