Question 27

If $$cot{2}$$A = x, then x is

Solution

Expression : $$cot(2A)$$

= $$\frac{cos(2A)}{sin(2A)}$$

$$\because$$ $$cos(2A)=cos^2A-sin^2A$$ and $$sin(2A)=2sinAcosA$$

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

Dividing both numerator and denominator by $$(sin^2A)$$

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

= $$(cot^2A-1)\div(2\frac{cosA}{sinA})$$

= $$\frac{cot^2A-1}{2cotA}$$

=> Ans - (B)

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