If 1/(cosecA ­+ cotA) = x, then the value of x is

Expression : $$\frac{1}{cosec A + cot A}$$

= $$\frac{1}{\frac{1}{sin A} + \frac{cos A}{sin A}}$$

= $$\frac{1}{\frac{1 + cos A}{sin A}} = \frac{sin A}{1 + cos A}$$

Multiplying both numerator and denominator by $$(1 - cos A)$$

= $$\frac{sin A}{1 + cos A} \times \frac{(1 - cos A)}{(1 - cos A)}$$

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

= $$\frac{1 - cos A}{sin A} = \frac{1}{sin A} - \frac{cos A}{sin A}$$

= $$cosec A - cot A$$

=> Ans - (B)