sin(3x+10)=cos(2x-40)

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Solution for sin(3x+10)=cos(2x-40) equation:


Simplifying
sin(3x + 10) = cos(2x + -40)

Reorder the terms:
ins(10 + 3x) = cos(2x + -40)
(10 * ins + 3x * ins) = cos(2x + -40)
(10ins + 3insx) = cos(2x + -40)

Reorder the terms:
10ins + 3insx = cos(-40 + 2x)
10ins + 3insx = (-40 * cos + 2x * cos)
10ins + 3insx = (-40cos + 2cosx)

Solving
10ins + 3insx = -40cos + 2cosx

Solving for variable 'i'.

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

Reorder the terms:
40cos + -2cosx + 10ins + 3insx = -40cos + 2cosx + 40cos + -2cosx

Reorder the terms:
40cos + -2cosx + 10ins + 3insx = -40cos + 40cos + 2cosx + -2cosx

Combine like terms: -40cos + 40cos = 0
40cos + -2cosx + 10ins + 3insx = 0 + 2cosx + -2cosx
40cos + -2cosx + 10ins + 3insx = 2cosx + -2cosx

Combine like terms: 2cosx + -2cosx = 0
40cos + -2cosx + 10ins + 3insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(40co + -2cox + 10in + 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 '(40co + -2cox + 10in + 3inx)' equal to zero and attempt to solve: Simplifying 40co + -2cox + 10in + 3inx = 0 Solving 40co + -2cox + 10in + 3inx = 0 Move all terms containing i to the left, all other terms to the right. Add '-40co' to each side of the equation. 40co + -2cox + 10in + -40co + 3inx = 0 + -40co Reorder the terms: 40co + -40co + -2cox + 10in + 3inx = 0 + -40co Combine like terms: 40co + -40co = 0 0 + -2cox + 10in + 3inx = 0 + -40co -2cox + 10in + 3inx = 0 + -40co Remove the zero: -2cox + 10in + 3inx = -40co Add '2cox' to each side of the equation. -2cox + 10in + 2cox + 3inx = -40co + 2cox Reorder the terms: -2cox + 2cox + 10in + 3inx = -40co + 2cox Combine like terms: -2cox + 2cox = 0 0 + 10in + 3inx = -40co + 2cox 10in + 3inx = -40co + 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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