What is the value of (cosecA - cotA) / (secA + tanA)?

Expression : (cosecA - cotA) / (secA + tanA)

Multiplying numerator and denominator by $$(sec A - tan A)$$

= $$\frac{cosec A - cot A}{sec A + tan A} \times \frac{sec A - tan A}{sec A - tan A}$$

= $$\frac{(cosec A - cot A) \times (sec A - tan A)}{sec^2 A - tan^2 A}$$

Now, $$(sec^2 A - tan^2 A) = (cosec^2 A - cot^2 A) = 1$$

= $$\frac{(cosec A - cot A) \times (sec A - tan A)}{cosec^2 A - cot^2 A}$$

= $$\frac{(cosec A - cot A) \times (sec A - tan A)}{(cosec A - cot A) \times (cosec A + cot A)}$$

= $$\frac{sec A - tan A}{cosec A + cot A}$$