If cosAcotA/(1 ­- sinA) = x, then the value of x is

Expression : cosAcotA/(1 ­- sinA) = x

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

Multiplying numerator and denominator by $$(1 + sin A)$$

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

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

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

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

=> Ans - (B)