Question

(1+cos2x)/(1-cos2x) = cot^2x

Answer 1

We will turn the left side into the right side.

`(1 + \cos 2x)/(1 - \cos2x) = \cot^2 x`

Use the identity:

`\cos 2x = \cos^2 x - \sin^2 x`

`(1 + \cos^2 x - \sin^2 x)/(1 - ( \cos^2 x - \sin^2 x)) = \cot^2 x`

`(1 - \sin^2 x + \cos^2 x )/(1 - \cos^2 x + \sin^2 x) = \cot^2 x`

Now use the identity

`\sin^2 x + \cos^2 x = 1` solved for sin^2 x and for cos^2 x.

`(\cos^2 x + \cos^2 x )/(\sin^2 x + \sin^2 x) = \cot^2 x`

`(2\cos^2 x)/(2\sin^2 x) = \cot^2 x`

`(\cos^2 x)/(\sin^2 x) = \cot^2 x`

`\cot^2 x = \cot^2 x`