Question

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

Answer 1

See explanation...

Explanation:

Given that:

`cos 2theta = cos^2 theta - sin^2 theta`

and:

`cos^2 theta + sin^2 theta = 1`

we find:

`cos 2theta = (1 - sin^2 theta) - sin^2 theta =1 - 2 sin^2 theta`