Question 95

What is the simplified value of (cosec A - sin A)(sec A - cos A)(tan A + cot A)?

Solution

Expression : (cosec A - sin A)(sec A - cos A)(tan A + cot A)

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

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

$$\because(sin^2A+cos^2A=1)$$

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

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

=> Ans - (C)

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