Sin(2x)=cos(x-45)

Solution for Sin(2x)=cos(x-45) equation:

Simplifying
Sin(2x) = cos(x + -45)

Remove parenthesis around (2x)
inS * 2x = cos(x + -45)

Reorder the terms for easier multiplication:
2inS * x = cos(x + -45)

Multiply inS * x
2inxS = cos(x + -45)

Reorder the terms:
2inxS = cos(-45 + x)
2inxS = (-45 * cos + x * cos)
2inxS = (-45cos + cosx)

Solving
2inxS = -45cos + cosx

Solving for variable 'i'.

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

Divide each side by '2nxS'.
i = -22.5cn-1osx-1S-1 + 0.5cn-1osS-1

Simplifying
i = -22.5cn-1osx-1S-1 + 0.5cn-1osS-1

Reorder the terms:
i = 0.5cn-1osS-1 + -22.5cn-1osx-1S-1