Prove that (cos2x +1)/sin2x = (sin 2x) / (1-cos2x)

Answer 1

desmos.com/calculator/q4mp8zm41f

The above graph uses Desmos to confirm the trig identity.

Answer 2

just cross multiply to get

sin^2(2x) = 1 - cos^2(2x)

use the trig identity: sin^2(x) + cos^2(x) = 1, which is equivalent to sin^2(x) = 1-cos^2(x)

just replace x with 2x to get

sin^2(2x) = 1 - cos^2(2x)

when you first cross multiply, that is multiply the denominator of the first fraction by the numerator of the 2nd fraction and set it equal to the numerator of the 1st fraction times the denominator of the 2nd fraction.

sin(2x) times sin(2x) = sin^2(2x)

cos(2x) -1 times 1+ cos(2x) = 1- cos^2(2x)