sin(3x+8)=cos(x+6)

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Solution for sin(3x+8)=cos(x+6) equation:


Simplifying
sin(3x + 8) = cos(x + 6)

Reorder the terms:
ins(8 + 3x) = cos(x + 6)
(8 * ins + 3x * ins) = cos(x + 6)
(8ins + 3insx) = cos(x + 6)

Reorder the terms:
8ins + 3insx = cos(6 + x)
8ins + 3insx = (6 * cos + x * cos)
8ins + 3insx = (6cos + cosx)

Solving
8ins + 3insx = 6cos + cosx

Solving for variable 'i'.

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

Reorder the terms:
-6cos + -1cosx + 8ins + 3insx = 6cos + cosx + -6cos + -1cosx

Reorder the terms:
-6cos + -1cosx + 8ins + 3insx = 6cos + -6cos + cosx + -1cosx

Combine like terms: 6cos + -6cos = 0
-6cos + -1cosx + 8ins + 3insx = 0 + cosx + -1cosx
-6cos + -1cosx + 8ins + 3insx = cosx + -1cosx

Combine like terms: cosx + -1cosx = 0
-6cos + -1cosx + 8ins + 3insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-6co + -1cox + 8in + 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 '(-6co + -1cox + 8in + 3inx)' equal to zero and attempt to solve: Simplifying -6co + -1cox + 8in + 3inx = 0 Solving -6co + -1cox + 8in + 3inx = 0 Move all terms containing i to the left, all other terms to the right. Add '6co' to each side of the equation. -6co + -1cox + 8in + 6co + 3inx = 0 + 6co Reorder the terms: -6co + 6co + -1cox + 8in + 3inx = 0 + 6co Combine like terms: -6co + 6co = 0 0 + -1cox + 8in + 3inx = 0 + 6co -1cox + 8in + 3inx = 0 + 6co Remove the zero: -1cox + 8in + 3inx = 6co Add 'cox' to each side of the equation. -1cox + 8in + cox + 3inx = 6co + cox Reorder the terms: -1cox + cox + 8in + 3inx = 6co + cox Combine like terms: -1cox + cox = 0 0 + 8in + 3inx = 6co + cox 8in + 3inx = 6co + cox 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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