Question 44

What is the simplified value of $$(\frac{2}{cot\frac{A}{2}+tan\frac{A}{2}})$$ ?

Solution

Expression : $$(\frac{2}{cot\frac{A}{2}+tan\frac{A}{2}})$$

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

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

= $$2\times sin\frac{A}{2}cos\frac{A}{2}$$

= $$sinA$$ [$$\because 2sin\theta cos\theta=sin2\theta$$]

=> Ans - (A)

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