Prove that: `(1+sin2theta+cos2theta)/(1+sin2theta-cos2theta)=cot theta`

Explanation

`=frac{1+sin 2 theta+cos 2 theta}{1+sin 2 theta-cos 2 theta}`


`= frac{(1+cos 2 theta)+sin 2 theta}{(1-cos 2 theta)+sin 2 theta} `


`= frac{2 cos ^{2} theta+2 sin theta cos theta}{2 sin ^{2} theta+2 sin theta cos theta} `


`= frac{2 cos theta(cos theta+sin theta)}{2 sin theta(sin theta+cos theta)}`


`= cot theta `