Question

How do you prove `cos2θ = 1-2sin²θ`?

Answer 1

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)`