1. sinx+cosx/tan^2x-1 = cos^2x/sinx-cosx

I've tried everything(converting to sines and cosines, factoring, etc.) and even my teacher couldn't figure it out...

2. 1+tanx/1-tanx = sec^2x+2tanx/2-sec^2x

I make everything more and more complicated when I try and verify this one from the right side