y=ln(1-cos(2x))

Solution for y=ln(1-cos(2x)) equation:

Simplifying
y = ln(1 + -1cos(2x))

Remove parenthesis around (2x)
y = ln(1 + -1cos * 2x)

Reorder the terms for easier multiplication:
y = ln(1 + -1 * 2cos * x)

Multiply -1 * 2
y = ln(1 + -2cos * x)

Multiply cos * x
y = ln(1 + -2cosx)
y = (1 * ln + -2cosx * ln)

Reorder the terms:
y = (-2clnosx + 1ln)
y = (-2clnosx + 1ln)

Solving
y = -2clnosx + 1ln

Solving for variable 'y'.

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

Simplifying
y = -2clnosx + 1ln