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

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


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

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

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

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

Solving for variable 'i'.

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

Reorder the terms:
20cos + -1cosx + 2ins + 3insx = -20cos + cosx + 20cos + -1cosx

Reorder the terms:
20cos + -1cosx + 2ins + 3insx = -20cos + 20cos + cosx + -1cosx

Combine like terms: -20cos + 20cos = 0
20cos + -1cosx + 2ins + 3insx = 0 + cosx + -1cosx
20cos + -1cosx + 2ins + 3insx = cosx + -1cosx

Combine like terms: cosx + -1cosx = 0
20cos + -1cosx + 2ins + 3insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(20co + -1cox + 2in + 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 + -1cox + 2in + 3inx)' equal to zero and attempt to solve:

Simplifying
20co + -1cox + 2in + 3inx = 0

Solving
20co + -1cox + 2in + 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 + -1cox + 2in + -20co + 3inx = 0 + -20co

Reorder the terms:
20co + -20co + -1cox + 2in + 3inx = 0 + -20co

Combine like terms: 20co + -20co = 0
0 + -1cox + 2in + 3inx = 0 + -20co
-1cox + 2in + 3inx = 0 + -20co
Remove the zero:
-1cox + 2in + 3inx = -20co

Add 'cox' to each side of the equation.
-1cox + 2in + cox + 3inx = -20co + cox

Reorder the terms:
-1cox + cox + 2in + 3inx = -20co + cox

Combine like terms: -1cox + cox = 0
0 + 2in + 3inx = -20co + cox
2in + 3inx = -20co + 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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