# How do you simplify the expression sin^2x/(1+cosx)?

Nov 27, 2016

The answer is $= 1 - \cos x$

#### Explanation:

We use

${\sin}^{2} x + {\cos}^{2} x = 1$

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

Therefore,

${\sin}^{2} \frac{x}{1 + \cos x} = \frac{\cancel{1 + \cos x} \left(1 - \cos x\right)}{\cancel{1 + \cos x}}$

$= 1 - \cos x$