Question 44

What is the simplified value of $$[\frac{2}{(cotA-tanA)}]$$

Solution

Expression : $$[\frac{2}{(cotA-tanA)}]$$

= $$2\div(cotA-tanA)$$

= $$2\div(\frac{cosA}{sinA}-\frac{sinA}{cosA})$$

= $$2\div(\frac{cos^2A-sin^2A}{sinAcosA})$$

= $$2\times(\frac{sinAcosA}{cos^2A-sin^2A})$$

= $$\frac{2sinAcosA}{cos^2A-sin^2A}$$

= $$\frac{sin2A}{cos2A}=tan2A$$

=> Ans - (B)

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