Question

How do you prove `cos2A = 2cos^2 A - 1`?

Answer 1

Probably it is not very much as a "proof" but...
if `A=30°`
`2A=60°`
so:
`cos(60°)=1/2`
`2cos^2(30°)-1=2(sqrt(3)/2)^2-1=3/2-1=1/2`