Question

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

Answer 1

Multiply, using the shortcut `(a + b)(a - b) = a^2 - b^2`.

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

Apply the pythagorean identity `sin^2theta + cos^2theta= 1 ->cos^2theta = 1- sin^2theta`:

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

Identity proved!

Hopefully this helps!