# How do you simplify (sin x + cos x)^2 + (sin x – cos x )^2?

Apr 17, 2016

See below

#### Explanation:

=sin^2x+2sinxcosx+cos^2x+sin^2x-2sinxcosx+cos^2x)

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

$= 2 \left({\sin}^{2} x + {\cos}^{2} x\right)$

$= 2 \cdot 1$

$= 2$