# Does this identity exist? If so, what is it equivalent to? -sin^(2)x+cos^(2)x = ?

Mar 18, 2018

$\cos \left(2 x\right)$

#### Explanation:

Yes this is an identity:

$- {\sin}^{2} x + {\cos}^{2} x =$

${\cos}^{2} x - {\sin}^{2} x =$

$\cos x \cos x - \sin x \sin x =$

Look familiar yet?

$\cos x \cos x - \sin x \sin x = \cos \left(2 x\right)$

Mar 18, 2018

$- {\sin}^{2} x + {\cos}^{2} x$

$= {\cos}^{2} x - {\sin}^{2} x$

$= {\cos}^{2} x - \left(1 - {\cos}^{2} x\right)$

$= 2 {\cos}^{2} x - 1$

$= \cos \left(2 x\right)$