How do you prove cos2θ = 1-2sin²θ?

1 Answer
Jun 13, 2015

Have a look:

Explanation:

Consider that:
cos(2theta)=cos^2(theta)-sin^2(theta)
So:
cos^2(theta)-sin^2(theta)=1-2sin^2(theta)
cos^2(theta)=1+sin^2(theta)-2sin^2(theta)
cos^2(theta)=1-sin^2(theta)
but: 1-sin^2(theta)=cos^2(theta)
So:
cos^2(theta)=cos^2(theta)