Question 94
If $$tan^{2}A/(secA-1)^{2}=x$$, then the value of x is
Solution
Expression : $$tan^{2}A/(secA-1)^{2}=x$$
= $$\frac{sin^2A}{cos^2A} \div (\frac{1}{cosA} - 1)^2$$
= $$\frac{sin^2A}{cos^2A} \div \frac{(1 - cosA)^2}{cos^2A}$$
= $$\frac{sin^2A}{cos^2A} \times \frac{cos^2A}{(1 - cosA)^2}$$
= $$\frac{1 - cos^2A}{(1 - cos A)^2} = \frac{(1 - cosA)(1 + cosA)}{(1 - cosA)^2}$$
= $$\frac{1 + cosA}{1 - cosA}$$
=> Ans - (C)
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