## How to prove this identity?

how would u proove this identity

$$\cos^2 \theta= \cos^2 - \sin^2= 2\cos^2\theta-1=1-2\sin^2\theta$$ ? The example i was given was $$\sin2\theta=2\sin\theta \cos\theta$$ this was a little bit easier to understand since there was a left and right side, im not sure how to proove this. How was this formula derived from the sum differnce formula?

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 cos(a+b) = cos(a)cos(b)-sin(a)sin(b) therefore cos(2a)=cos(a)cos(a)-sin(a)sin(a) this is the first step... the rest should be easy