sin(2x+30)=cos(2x+15)

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Solution for sin(2x+30)=cos(2x+15) equation:


Simplifying
sin(2x + 30) = cos(2x + 15)

Reorder the terms:
ins(30 + 2x) = cos(2x + 15)
(30 * ins + 2x * ins) = cos(2x + 15)
(30ins + 2insx) = cos(2x + 15)

Reorder the terms:
30ins + 2insx = cos(15 + 2x)
30ins + 2insx = (15 * cos + 2x * cos)
30ins + 2insx = (15cos + 2cosx)

Solving
30ins + 2insx = 15cos + 2cosx

Solving for variable 'i'.

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

Reorder the terms:
-15cos + -2cosx + 30ins + 2insx = 15cos + 2cosx + -15cos + -2cosx

Reorder the terms:
-15cos + -2cosx + 30ins + 2insx = 15cos + -15cos + 2cosx + -2cosx

Combine like terms: 15cos + -15cos = 0
-15cos + -2cosx + 30ins + 2insx = 0 + 2cosx + -2cosx
-15cos + -2cosx + 30ins + 2insx = 2cosx + -2cosx

Combine like terms: 2cosx + -2cosx = 0
-15cos + -2cosx + 30ins + 2insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-15co + -2cox + 30in + 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 '(-15co + -2cox + 30in + 2inx)' equal to zero and attempt to solve: Simplifying -15co + -2cox + 30in + 2inx = 0 Solving -15co + -2cox + 30in + 2inx = 0 Move all terms containing i to the left, all other terms to the right. Add '15co' to each side of the equation. -15co + -2cox + 30in + 15co + 2inx = 0 + 15co Reorder the terms: -15co + 15co + -2cox + 30in + 2inx = 0 + 15co Combine like terms: -15co + 15co = 0 0 + -2cox + 30in + 2inx = 0 + 15co -2cox + 30in + 2inx = 0 + 15co Remove the zero: -2cox + 30in + 2inx = 15co Add '2cox' to each side of the equation. -2cox + 30in + 2cox + 2inx = 15co + 2cox Reorder the terms: -2cox + 2cox + 30in + 2inx = 15co + 2cox Combine like terms: -2cox + 2cox = 0 0 + 30in + 2inx = 15co + 2cox 30in + 2inx = 15co + 2cox 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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