sin(2x-30)=cos(3x+10)

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Solution for sin(2x-30)=cos(3x+10) equation: 


Simplifying
sin(2x + -30) = cos(3x + 10)

Reorder the terms:
ins(-30 + 2x) = cos(3x + 10)
(-30 * ins + 2x * ins) = cos(3x + 10)
(-30ins + 2insx) = cos(3x + 10)

Reorder the terms:
-30ins + 2insx = cos(10 + 3x)
-30ins + 2insx = (10 * cos + 3x * cos)
-30ins + 2insx = (10cos + 3cosx)

Solving
-30ins + 2insx = 10cos + 3cosx

Solving for variable 'i'.

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

Reorder the terms:
-10cos + -3cosx + -30ins + 2insx = 10cos + 3cosx + -10cos + -3cosx

Reorder the terms:
-10cos + -3cosx + -30ins + 2insx = 10cos + -10cos + 3cosx + -3cosx

Combine like terms: 10cos + -10cos = 0
-10cos + -3cosx + -30ins + 2insx = 0 + 3cosx + -3cosx
-10cos + -3cosx + -30ins + 2insx = 3cosx + -3cosx

Combine like terms: 3cosx + -3cosx = 0
-10cos + -3cosx + -30ins + 2insx = 0

Factor out the Greatest Common Factor (GCF), 's'.
s(-10co + -3cox + -30in + 2inx) = 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 '(-10co + -3cox + -30in + 2inx)' equal to zero and attempt to solve:

Simplifying
-10co + -3cox + -30in + 2inx = 0

Solving
-10co + -3cox + -30in + 2inx = 0

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

Add '10co' to each side of the equation.
-10co + -3cox + -30in + 10co + 2inx = 0 + 10co

Reorder the terms:
-10co + 10co + -3cox + -30in + 2inx = 0 + 10co

Combine like terms: -10co + 10co = 0
0 + -3cox + -30in + 2inx = 0 + 10co
-3cox + -30in + 2inx = 0 + 10co
Remove the zero:
-3cox + -30in + 2inx = 10co

Add '3cox' to each side of the equation.
-3cox + -30in + 3cox + 2inx = 10co + 3cox

Reorder the terms:
-3cox + 3cox + -30in + 2inx = 10co + 3cox

Combine like terms: -3cox + 3cox = 0
0 + -30in + 2inx = 10co + 3cox
-30in + 2inx = 10co + 3cox

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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