Question

cos2x=cos^2x-1/2

Answer 1

\[\frac12(1+\cos(2x))=\cos^2x\]

Answer 2

Wow, Turing!! how do you derive that? :P

Answer 3

I would like to know as well

Answer 4

\[\cos \left( 2x \right)=\cos \left( x+x \right)=\cos ^{2}x-\sin ^{2}x=2\cos ^{2}x-1\]\[2\cos^{2}x - 1 =\cos \left( 2x \right)\]\[\cos^{2}x=\frac{1}{2}\left( 1+\cos \left( 2x \right) \right)\]

Answer 5

Whats the exact angle for this?

Answer 6

sorry for not deriving that earlier
I use that formula so often for integration I forget it's not so commonly known in precalc
thanks @extraven for filling in the missing proof!

Answer 7

^ @exraven I meant. oops :/

Answer 8

you are welcome :)