# How do I simplify this expression? sin^2x-cos^2x/sinx-cosx

Mar 18, 2018

$\sin x + \cos x$

#### Explanation:

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

Since the numerator has a difference of squares:
$\left({a}^{2} - {b}^{2}\right) = \left(a + b\right) \cdot \left(a - b\right)$

$\frac{\left(\sin x - \cos x\right) \left(\sin x + \cos x\right)}{\sin x - \cos x} =$

$\frac{\left(\cancel{\sin x - \cos x}\right) \left(\sin x + \cos x\right)}{\cancel{\sin x - \cos x}} =$

$\sin x + \cos x$