Question

differentiation of cosx / 1+sinx

Answer 1

$\frac{cosx}{1 + sinx} = \frac{cosx(1 - sinx)}{(1 + sinx)(1 - sinx)}$

$= \frac{cosx(1 - sinx)}{1 - {sin}^{2}x } = \frac{cosx(1 - sinx)}{ {cos}^{2}x }$

$= \frac{1 - sinx}{cosx} = secx - tanx$

Therefore,

Differentitation w. r. t. x

$secx.tanx - {sec}^{2} x$