# How do I show this equation is not an identity in paragraph form? sin α=square root 1-cos²α

Mar 23, 2018

Can't really do that, because this is a true statement

#### Explanation:

Using the identity:
${\sin}^{2} \alpha + {\cos}^{2} \alpha = 1$

Start:

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

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

$\sin \alpha = \sqrt{{\sin}^{2} \alpha \cancel{+ {\cos}^{2} \alpha} \cancel{- {\cos}^{2} \alpha}}$

$\sin \alpha = \sqrt{{\sin}^{2} \alpha}$

$\sin \alpha = \sin \alpha$