A) \[\operatorname{cosec}\,\theta \]
B) \[2\operatorname{cosec}\,\theta \]
C) \[sec\,\theta \]
D) \[2sec\,\theta \]
Correct Answer: B
Solution :
\[\frac{\tan \theta }{\sec \theta -1}+\frac{\tan \theta }{\sec \theta +1}=\tan \theta \left\{ \frac{(\sec \theta +1)+(\sec \theta -1)}{{{\sec }^{2}}\theta -1} \right\}\] \[=\frac{\tan \theta .2\sec \theta }{{{\tan }^{2}}\theta }\] \[=2\frac{\sec \theta }{\tan \theta }\] \[=2\operatorname{coses}\,\theta \]
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