sin(3x+20)=cos(7x-30)

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Solution for sin(3x+20)=cos(7x-30) equation: 


Simplifying
sin(3x + 20) = cos(7x + -30)

Reorder the terms:
ins(20 + 3x) = cos(7x + -30)
(20 * ins + 3x * ins) = cos(7x + -30)
(20ins + 3insx) = cos(7x + -30)

Reorder the terms:
20ins + 3insx = cos(-30 + 7x)
20ins + 3insx = (-30 * cos + 7x * cos)
20ins + 3insx = (-30cos + 7cosx)

Solving
20ins + 3insx = -30cos + 7cosx

Solving for variable 'i'.

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

Reorder the terms:
30cos + -7cosx + 20ins + 3insx = -30cos + 7cosx + 30cos + -7cosx

Reorder the terms:
30cos + -7cosx + 20ins + 3insx = -30cos + 30cos + 7cosx + -7cosx

Combine like terms: -30cos + 30cos = 0
30cos + -7cosx + 20ins + 3insx = 0 + 7cosx + -7cosx
30cos + -7cosx + 20ins + 3insx = 7cosx + -7cosx

Combine like terms: 7cosx + -7cosx = 0
30cos + -7cosx + 20ins + 3insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(30co + -7cox + 20in + 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 '(30co + -7cox + 20in + 3inx)' equal to zero and attempt to solve:

Simplifying
30co + -7cox + 20in + 3inx = 0

Solving
30co + -7cox + 20in + 3inx = 0

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

Add '-30co' to each side of the equation.
30co + -7cox + 20in + -30co + 3inx = 0 + -30co

Reorder the terms:
30co + -30co + -7cox + 20in + 3inx = 0 + -30co

Combine like terms: 30co + -30co = 0
0 + -7cox + 20in + 3inx = 0 + -30co
-7cox + 20in + 3inx = 0 + -30co
Remove the zero:
-7cox + 20in + 3inx = -30co

Add '7cox' to each side of the equation.
-7cox + 20in + 7cox + 3inx = -30co + 7cox

Reorder the terms:
-7cox + 7cox + 20in + 3inx = -30co + 7cox

Combine like terms: -7cox + 7cox = 0
0 + 20in + 3inx = -30co + 7cox
20in + 3inx = -30co + 7cox

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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