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

Jan 4, 2017

see below

#### Explanation:

$\textcolor{red}{\left(1 + \sin \alpha\right) \left(1 - \sin \alpha\right)} = {\cos}^{2} \alpha$

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 :)

$1 - {\sin}^{2} \alpha = {\cos}^{2} \alpha \implies {\sin}^{2} \alpha + {\cos}^{2} \alpha = 1$