A) \[\frac{1}{2}\]
B) \[2\]
C) \[\frac{1}{4}\]
D) \[4\]
Correct Answer: A
Solution :
| [a] We have, \[2x=\sec \theta \] and \[\frac{2}{x}=\tan \theta \] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x=\frac{\sec \theta }{2}\] and \[\frac{1}{x}=\frac{\tan \theta }{2}\] .(1) |
| \[\therefore \,\,\,\,\,\,\,\,\,\,2\left( {{x}^{2}}-\frac{1}{{{x}^{2}}} \right)=2\left( \frac{{{\sec }^{2}}\theta }{4}-\frac{{{\tan }^{2}}\theta }{4} \right)\] (From eq. (1)) |
| \[=\frac{2}{4}({{\sec }^{2}}\theta -{{\tan }^{2}}\theta )=\frac{1}{2}\cdot 1\] \[[{{\sec }^{2}}\theta -{{\tan }^{2}}\theta =1]\] |
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