Question

please prove this problem​

Answer 1

Step-by-step explanation:

We have,

$\frac{ \sin( \theta) }{1 - \cot( \theta) } + \frac{ \cos( \theta) }{1 - \tan( \theta) }$

$= \frac{ \sin( \theta) }{1 - \frac{1 }{ \tan( \theta) }} + \frac{ \cos( \theta) }{1 - \tan( \theta) }$

$= - \frac{ \sin( \theta) \tan( \theta) }{1 - \tan( \theta) } + \frac{ \cos( \theta) }{1 - \tan( \theta) }$

$= \frac{ \cos( \theta ) - \sin( \theta) \tan( \theta) }{1 - \tan( \theta) }$

$= \frac{ \cos( \theta ) - \frac{ \sin( \theta) }{ \cos (\theta)} }{1 - \tan( \theta) }$

$= \frac{ \cos^{2} ( \theta ) - \sin^{2} ( \theta) }{ \cos( \theta) (1 - \tan( \theta)) }$

$= \frac{ (\cos( \theta ) - \sin ( \theta)) ( \cos( \theta) + \sin( \theta) ) }{( \cos( \theta) - \sin( \theta)) }$

$= \cos( \theta) + \sin( \theta)$

Answer 2

Your answer with complete solution is in above photos