Question

prove
$\frac{ \cot {x}^{2} (\sec(x) - 1) ) }{1 + \sin(x) } = \frac{ \sec {x}^{2} (1 - \sin(x) ) }{1 + \sec(x) }$
and
$\sqrt{ \frac{ \tan(x) + \sin(x) }{ \cot(x) - \cos(x) } } = \tan {x}^{2} \sqrt{ \frac{1 + \sin(x) }{1 - \cos(x) } }$
please thank you