1. ## Identities help...

I'm stuck on this question:

Prove identity: 1-tanѲsin2Ѳ=cos2Ѳ

I understand i have to use this formula sin 2A=2sinAcosA but i don't know what to do from there..

2. We have $\cos\theta=\cos^2\theta-\sin^2\theta=2\cos^2\theta-1=1-2\sin^2\theta$

Now, $1-\tan\theta\sin 2\theta=1-\frac{\sin\theta}{\cos\theta}\cdot 2\sin\theta\cos\theta=1-2\sin^2\theta=\cos 2\theta$