Question 96

What is the simplified value of $$\sqrt{\frac{1}{sin^2A}+\frac{1}{cos^2A}}$$ ?

Solution

Expression : $$\sqrt{\frac{1}{sin^2A}+\frac{1}{cos^2A}}$$

= $$\sqrt{\frac{sin^2A+cos^2A}{sin^2A.cos^2A}}$$

= $$\sqrt{\frac{1}{sin^2A.cos^2A}}=\frac{1}{sinA.cosA}$$

= $$\frac{sin^2A+cos^2A}{sinA.cosA}$$

= $$\frac{sin^2A}{sinA.cosA}+\frac{cos^2A}{sinA.cosA}$$

= $$\frac{sinA}{cosA}+\frac{cosA}{sinA}=tanA+cotA$$

=> Ans - (B)

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