Question

How do you prove `cos ^2 theta - sin ^2 theta = 2 cos^2 theta -1`?

Answer 1

Try this:

Explanation:

I would use:
`sin^2(theta)+cos^2(theta)=1`
and so:
`sin^2(theta)=1-cos^2(theta)`
in your expression:
`cos^2(theta)-1+cos^2(theta)=2cos^2(theta)-1`
and:
`2cos^2(theta)-1=2cos^2(theta)-1`