A) \[\theta \]
B) \[\frac{\theta }{2}\]
C) \[\frac{\pi }{2}-\theta \]
D) \[\frac{\pi }{2}-\frac{\theta }{2}\]
Correct Answer: C
Solution :
\[\theta ={{\tan }^{-1}}\left( \frac{2\sqrt{1-{{\sin }^{2}}\theta }}{2\sin \theta } \right)={{\tan }^{-1}}\left( \frac{\cos \theta }{\sin \theta } \right)\] \[{{\tan }^{-1}}\left\{ \tan \left( \frac{\pi }{2}-\theta \right) \right\}=\frac{\pi }{2}-\theta \] .
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