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JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Trigonometrical ratios of multiple and sub multiple angles

  • question_answer
    If \[\tan A=\frac{1-\cos B}{\sin B},\]find\[\tan 2A\]in terms of \[\tan B\]and show that [IIT 1983; MP PET 1994]

    A) \[\tan 2A=\tan B\]

    B) \[\tan 2A={{\tan }^{2}}B\]

    C) \[\tan 2A={{\tan }^{2}}B+2\tan B\]

    D) None of the above

    Correct Answer: A

    Solution :

    \[\tan A=\frac{1-\cos B}{\sin B}=\frac{2{{\sin }^{2}}(B/2)}{2\sin (B/2)\cos (B/2)}=\tan \frac{B}{2}\] Þ \[\tan 2A=\tan B\].


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