RAJASTHAN ­ PET Rajasthan PET Solved Paper-2007

  • question_answer The value of\[\tan \left\{ {{\cos }^{-1}}\left( -\frac{2}{7} \right)-\frac{\pi }{2} \right\}\]is

    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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