Question

please prove it with step by step explanation.

Answer 1

L.H.S
$\frac{1}{ \csc(x) - \cot(x) } - \frac{1}{ \sin(x) } \\ \frac{1}{ \csc(x) - \cot(x) } \times \frac{ \csc(x) + \cot(x) }{ \csc(x) + \cot(x) } - \csc(x) \\ \frac{ \csc(x) + \cot(x) }{ \csc(x) {}^{2} - \cot(x) {}^{2} } \\ \csc(x) + \cot(x) - \csc(x) \\ \cot(x)$
R.H.S
$\frac{1}{ \sin(x) } - ( \frac{1}{ \csc(x) + \cot(x) } \times \frac{ \csc(x) - \cot(x) }{ \csc(x) - \cot(x) } \\ \csc(x) - ( \frac{ \csc(x) - \cot(x) }{ { \csc(x) }^{2} - \cot(x) {}^{2} } \\ \csc(x) - \csc(x) + \cot(x) \\ \cot(x)$
L.H.S=R.H.S.
hope this helps you:-))))
don't forget to do it brainleist.