A) \[\frac{2}{3\sqrt{5}}\]
B) \[\frac{2}{3}\]
C) \[\frac{1}{\sqrt{5}}\]
D) \[\frac{4}{\sqrt{5}}\]
Correct Answer: A
Solution :
\[\tan \left\{ {{\cos }^{-1}}\left( -\frac{2}{7} \right)-\frac{\pi }{2} \right\}\] \[=\tan \left\{ \pi -{{\cos }^{-1}}\left( \frac{2}{7} \right)-\frac{\pi }{2} \right\}\] \[=\tan \left\{ \frac{\pi }{2}-{{\cos }^{-1}}\left( \frac{2}{7} \right) \right\}\] \[=\tan \left\{ {{\sin }^{-1}}\frac{2}{7} \right\}\] \[=\tan \left\{ {{\tan }^{-1}}\left( \frac{2}{3\sqrt{5}} \right) \right\}\] \[=\frac{2}{3\sqrt{5}}\]
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