1) 2sin^2 x+sin2x=1 find x for 0<x<pi

2) prove that (1+tan$\displaystyle \theta$)(1+tan($\displaystyle \pi$/4-$\displaystyle \theta$))=2

3) prove $\displaystyle \frac{{sinx}}{{1-cosx}}=cot\frac{{x}}{{2}}$

I've been working on this all afternoon and my solution still doesn't match with the answers