Question 85

(cosecA - sinA)(secA - cosA)(tanA + cotA) is equals to

Solution

Expression : (cosecA - sinA)(secA - cosA)(tanA + cotA)

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

= $$(\frac{1-sin^2A}{sinA})(\frac{1-cos2^A}{cosA})(\frac{sin^2A+cos^2A}{sinAcosA})$$

Using, $$(sin^2A+cos^2A = 1)$$

= $$\frac{cos^2A}{sinA} \times \frac{sin^2A}{cosA} \times \frac{1}{sinAcosA}$$

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

=> Ans - (C)

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