Question

How do you verify the identity `(1+sinalpha)(1-sinalpha)=cos^2alpha`?

Answer 1

see below

Explanation:

`color(red)((1+sinalpha)(1-sinalpha))=cos^2alpha`

apply FOIL to the red bit. you get: `1 - sin alpha + sin alpha - sin^2 alpha = 1 - sin^2 alpha`

then you have the Pythagorean identity to finish it off :)

`1 - sin^2 alpha = cos^2 alpha implies sin^2 alpha + cos^2 alpha = 1`