Question 77

What is the simplest form of (1 + cosA)(cosecA - cotA)?

Solution

Expression : (1 + cosA)(cosecA - cotA)

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

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

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

= $$sinA$$

=> Ans - (D)

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