1/(tanA + cotA) is equal to ?

Expression : 1/(tanA + cotA)

= $$1 \div (\frac{sinA}{cosA}+\frac{cosA}{sinA})$$

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

= $$1 \times sinAcosA=sinAcosA$$

Multiplying and dividing by $$(sinAcosA)$$

= $$\frac{sin^2Acos^2A}{sinAcosA} = (\frac{cos^2A}{sinA} \times \frac{sin^2A}{cosA})$$

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

= $$(\frac{1}{sinA}-sinA) \times (\frac{1}{cosA}-cosA)$$

= $$(cosecA-sinA)(secA-cosA)$$

=> Ans - (D)