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SSC Sample Paper SSC-CGL TIER - I Sample Test Paper-9

  • question_answer
    If\[\tan \,A=\frac{1-\cos \,B}{\sin \,B}\], then what is \[\,\frac{2\,\tan \,A}{1-{{\tan }^{2}}\,A}\,\]equal to?

    A) \[\frac{(tan\,B)}{2}\]                             

    B) 2 tan B

    C)

    D) 4 tan B

    Correct Answer: C

    Solution :

    \[\tan A=\frac{1-\cos \,B}{\sin \,B}\] =         \[\frac{2{{\sin }^{2}}B/2}{2\sin B/2\cos B/2}\] =         \[\tan \,\,B/2\Rightarrow A=\frac{B}{2}\] Now, \[\frac{2\,\,\operatorname{tanA}}{1-{{\tan }^{2}}A}=\tan \,\,2A\] =         \[\tan \,\,2\times \frac{B}{2}=\tan B\] tan B                           


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