Question

Prove that: $\frac{1+\sin 2\theta -\cos 2\theta }{1+\sin 2\theta +\cos 2\theta }=\tan \theta$

Answer 1

L.H.S=$=(1-\cos 2\theta )+\sin 2\theta (1-\cos 2\theta )+\sin 2\theta =2\sin 2\theta +2\sin \theta \cos \theta 2\cos 2\theta +2\sin \theta \cos \theta =\tan \theta$= R.H.S