Question

How do you verify the identity `cos^2beta-sin^2beta=1-2sin^2beta`?

Answer 1

see below

Explanation:

Left Hand Side:

Use the identity `sin^2 beta + cos^2 beta = 1`

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

`=1-sin^2 beta -sin^2 beta`

`=1-2 sin^2 beta`

`:.=` Right Hand Side