Answer
Differentiate $f(\theta ) = \frac{\sin \theta}{1 + \cos \theta}$
$f'(\theta )=\frac {1}{1+\cos \theta}$
Work Step by Step
Differentiate using quotient rule and the trig rules.
$f'(\theta ) = \frac{\sin \theta '(1+\cos \theta) - \sin \theta (\cos \theta ') }{(1 +\cos \theta)^2}$
$= \frac{\cos \theta(1+\cos \theta) - \sin \theta (-\sin \theta)}{(1 +\cos \theta)^2}$
$=\frac{\cos \theta + \cos ^2 \theta +\sin ^2 \theta}{(1 +\cos \theta)^2}$
Simplify using trig identities
$=\frac{1+\cos \theta}{(1 +\cos \theta)^2}$
$=\frac {1}{1+\cos \theta}$
