# How do you prove the identity -sin^2x = 2cosx - 2?

Aug 12, 2015

The given expression is not a valid indentity
$\textcolor{w h i t e}{\text{XXXX}}$(It can not be proven).

#### Explanation:

Consider, for example $x = \frac{\pi}{2}$

$\textcolor{w h i t e}{\text{XXXX}}$$- {\sin}^{2} \left(\frac{\pi}{2}\right) = - 1$

$\textcolor{w h i t e}{\text{XXXX}}$$2 \cos \left(\frac{\pi}{2}\right) - 2 = - 2$

$- \sin \left(\frac{\pi}{2}\right) \ne 2 \cos \left(\frac{\pi}{2}\right) - 2$