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

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


Simplifying
sin(2x) + -1cos(2x) = sin(3x) + cos(x) + -2

Remove parenthesis around (2x)
ins * 2x + -1cos(2x) = sin(3x) + cos(x) + -2

Reorder the terms for easier multiplication:
2ins * x + -1cos(2x) = sin(3x) + cos(x) + -2

Multiply ins * x
2insx + -1cos(2x) = sin(3x) + cos(x) + -2

Remove parenthesis around (2x)
2insx + -1cos * 2x = sin(3x) + cos(x) + -2

Reorder the terms for easier multiplication:
2insx + -1 * 2cos * x = sin(3x) + cos(x) + -2

Multiply -1 * 2
2insx + -2cos * x = sin(3x) + cos(x) + -2

Multiply cos * x
2insx + -2cosx = sin(3x) + cos(x) + -2

Reorder the terms:
-2cosx + 2insx = sin(3x) + cos(x) + -2

Remove parenthesis around (3x)
-2cosx + 2insx = ins * 3x + cos(x) + -2

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

Multiply ins * x
-2cosx + 2insx = 3insx + cos(x) + -2

Multiply cos * x
-2cosx + 2insx = 3insx + cosx + -2

Reorder the terms:
-2cosx + 2insx = -2 + cosx + 3insx

Solving
-2cosx + 2insx = -2 + cosx + 3insx

Solving for variable 'c'.

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

Add '-1cosx' to each side of the equation.
-2cosx + -1cosx + 2insx = -2 + cosx + -1cosx + 3insx

Combine like terms: -2cosx + -1cosx = -3cosx
-3cosx + 2insx = -2 + cosx + -1cosx + 3insx

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

Add '-2insx' to each side of the equation.
-3cosx + 2insx + -2insx = -2 + 3insx + -2insx

Combine like terms: 2insx + -2insx = 0
-3cosx + 0 = -2 + 3insx + -2insx
-3cosx = -2 + 3insx + -2insx

Combine like terms: 3insx + -2insx = 1insx
-3cosx = -2 + 1insx

Divide each side by '-3osx'.
c = 0.6666666667o-1s-1x-1 + -0.3333333333ino-1

Simplifying
c = 0.6666666667o-1s-1x-1 + -0.3333333333ino-1

Reorder the terms:
c = -0.3333333333ino-1 + 0.6666666667o-1s-1x-1

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