# Identities help...

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• Nov 12th 2008, 05:57 PM
eh501
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..
• Nov 13th 2008, 08:30 AM
red_dog
We have $\cos\theta=\cos^2\theta-\sin^2\theta=2\cos^2\theta-1=1-2\sin^2\theta$

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