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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