sin(2x+30)=cos(8x-40)

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Solution for sin(2x+30)=cos(8x-40) equation:


Simplifying
sin(2x + 30) = cos(8x + -40)

Reorder the terms:
ins(30 + 2x) = cos(8x + -40)
(30 * ins + 2x * ins) = cos(8x + -40)
(30ins + 2insx) = cos(8x + -40)

Reorder the terms:
30ins + 2insx = cos(-40 + 8x)
30ins + 2insx = (-40 * cos + 8x * cos)
30ins + 2insx = (-40cos + 8cosx)

Solving
30ins + 2insx = -40cos + 8cosx

Solving for variable 'i'.

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

Reorder the terms:
40cos + -8cosx + 30ins + 2insx = -40cos + 8cosx + 40cos + -8cosx

Reorder the terms:
40cos + -8cosx + 30ins + 2insx = -40cos + 40cos + 8cosx + -8cosx

Combine like terms: -40cos + 40cos = 0
40cos + -8cosx + 30ins + 2insx = 0 + 8cosx + -8cosx
40cos + -8cosx + 30ins + 2insx = 8cosx + -8cosx

Combine like terms: 8cosx + -8cosx = 0
40cos + -8cosx + 30ins + 2insx = 0

Factor out the Greatest Common Factor (GCF), '2s'.
2s(20co + -4cox + 15in + inx) = 0

Ignore the factor 2.

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 '(20co + -4cox + 15in + inx)' equal to zero and attempt to solve: Simplifying 20co + -4cox + 15in + inx = 0 Solving 20co + -4cox + 15in + inx = 0 Move all terms containing i to the left, all other terms to the right. Add '-20co' to each side of the equation. 20co + -4cox + 15in + -20co + inx = 0 + -20co Reorder the terms: 20co + -20co + -4cox + 15in + inx = 0 + -20co Combine like terms: 20co + -20co = 0 0 + -4cox + 15in + inx = 0 + -20co -4cox + 15in + inx = 0 + -20co Remove the zero: -4cox + 15in + inx = -20co Add '4cox' to each side of the equation. -4cox + 15in + 4cox + inx = -20co + 4cox Reorder the terms: -4cox + 4cox + 15in + inx = -20co + 4cox Combine like terms: -4cox + 4cox = 0 0 + 15in + inx = -20co + 4cox 15in + inx = -20co + 4cox 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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