Question 96

If $$2cosec^2A = x$$, then the value of x is

Solution

Expression : $$2cosec^2A = x$$

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

Adding and Subtracting $$(cosA)$$ in the numerator

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

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

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

= $$\frac{1}{1-cosA} + \frac{1}{1+cosA}$$

=> Ans - (C)

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