Question 71

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

Solution

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

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

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

= $$\frac{(1+sinA) + (1-sinA)}{1 - sin^2A}$$

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

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

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

=> Ans - (C)

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