sin(3x-10)=cos(2x+20)

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Solution for sin(3x-10)=cos(2x+20) equation: 


Simplifying
sin(3x + -10) = cos(2x + 20)

Reorder the terms:
ins(-10 + 3x) = cos(2x + 20)
(-10 * ins + 3x * ins) = cos(2x + 20)
(-10ins + 3insx) = cos(2x + 20)

Reorder the terms:
-10ins + 3insx = cos(20 + 2x)
-10ins + 3insx = (20 * cos + 2x * cos)
-10ins + 3insx = (20cos + 2cosx)

Solving
-10ins + 3insx = 20cos + 2cosx

Solving for variable 'i'.

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

Reorder the terms:
-20cos + -2cosx + -10ins + 3insx = 20cos + 2cosx + -20cos + -2cosx

Reorder the terms:
-20cos + -2cosx + -10ins + 3insx = 20cos + -20cos + 2cosx + -2cosx

Combine like terms: 20cos + -20cos = 0
-20cos + -2cosx + -10ins + 3insx = 0 + 2cosx + -2cosx
-20cos + -2cosx + -10ins + 3insx = 2cosx + -2cosx

Combine like terms: 2cosx + -2cosx = 0
-20cos + -2cosx + -10ins + 3insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-20co + -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 '(-20co + -2cox + -10in + 3inx)' equal to zero and attempt to solve:

Simplifying
-20co + -2cox + -10in + 3inx = 0

Solving
-20co + -2cox + -10in + 3inx = 0

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

Add '20co' to each side of the equation.
-20co + -2cox + -10in + 20co + 3inx = 0 + 20co

Reorder the terms:
-20co + 20co + -2cox + -10in + 3inx = 0 + 20co

Combine like terms: -20co + 20co = 0
0 + -2cox + -10in + 3inx = 0 + 20co
-2cox + -10in + 3inx = 0 + 20co
Remove the zero:
-2cox + -10in + 3inx = 20co

Add '2cox' to each side of the equation.
-2cox + -10in + 2cox + 3inx = 20co + 2cox

Reorder the terms:
-2cox + 2cox + -10in + 3inx = 20co + 2cox

Combine like terms: -2cox + 2cox = 0
0 + -10in + 3inx = 20co + 2cox
-10in + 3inx = 20co + 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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