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JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer
    If \[A+C=B,\] then \[\tan A\,\tan B\,\tan C=\] [EAMCET 1986]

    A) \[\tan A\,\tan B+\tan \,C\]

    B) \[\tan \,B-\tan \,C-\tan \,A\]

    C) \[\tan A+\tan C-\tan B\]

    D) \[-\,(\tan A\tan B+\tan C)\]

    Correct Answer: B

    Solution :

    \[B=A+C\Rightarrow \tan B=\tan (A+C)\] Þ \[\tan B=\frac{\tan A+\tan C}{1-\tan A\tan C}\] Þ \[\tan A\tan B\tan C=\tan B-\tan A-\tan C\].


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