Question 95

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

Solution

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

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

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

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

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

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

=> Ans - (B)

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