#### Answer

Differentiate $y=\frac{\sin t}{1 +\tan t}$
$y'=\frac{\cos t + \sin t -\tan t\sec t}{(1+\tan t)^2}$

#### Work Step by Step

Differentiate using quotient rule and trig rules.
$y' =\frac{\cos t(1+\tan t) - \sin t(\sec ^2t)}{(1+\tan t)^2}$
$=\frac{\cos t + \sin t -\tan t\sec t}{(1+\tan t)^2}$