Question

Someone please solve it fast it's urgent .

Answer 1

Hey !!!

solution is in this attachment

__________________________

Hope it helps you !!!


@Rajukumar111

Answer 2

Solution-

L.H.S

$=\frac{1}{\csc x-\cot x}-\frac{1}{\sin x}$

$= \frac{(\csc x+\cot x)}{(\csc x-\cot x)(\csc x+\cot x)}-\frac{1}{\sin x}$

$= \frac{(\csc x+\cot x)}{(\csc^2 x-\cot^2 x)}-\frac{1}{\sin x}$

$= \csc x+\cot x-\frac{1}{\sin x}$

$=\frac{1+\cos x -1}{\sin x}$

$=\cot x$

R.H.S

$=\frac{1}{\sin x}-\frac{1}{\csc x+\cot x}$

$= \frac{1}{\sin x}-\frac{(\csc x-\cot x)}{(\csc x+\cot x)(\csc x-\cot x)}$

$= \frac{1}{\sin x}-\frac{(\csc x-\cot x)}{(\csc^2 x-\cot^2 x)}$

$= \frac{1}{\sin x}-\csc x+\cot x$

$=\frac{1-1+\cos x}{\sin x}$

$=\cot x$

∴L.H.S = R.H.S