1/(secA + tanA) is equal to

Expression : 1/(secA + tanA)

= $$\frac{1}{\frac{1}{cosA} + \frac{sinA}{cosA}}$$

= $$\frac{1}{\frac{1+sinA}{cosA}} = \frac{cosA}{1+sinA}$$

Multiplying both numerator and denominator by $$(1-sinA)$$

= $$\frac{cosA}{1+sinA} \times \frac{1-sinA}{1-sinA}$$

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

= $$\frac{1-sinA}{cosA} = \frac{1}{cosA} - \frac{sinA}{cosA}$$

= $$secA-tanA$$

=> Ans - (C)