Question

How do you verify `(1+sin theta)(1- sin theta) = cos^2 theta`?

Answer 1

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

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

Modifying the pythagorean identity `sin^2x + cos^2x = 1 -> cos^2x = 1 - sin^2x`:

`cos^2theta = cos^2theta`

Identity proved!

Hopefully this helps!