11th Class Mathematics Trigonometric Identities Question Bank Critical Thinking

  • question_answer If \[A+B+C=\pi \] and \[\cos A=\cos B\,\cos C,\] then \[\tan B\,\,\tan C\] is equal to [AMU 2001]

    A) \[\frac{1}{2}\]

    B) 2

    C) 1

    D) \[-\frac{1}{2}\]

    Correct Answer: B

    Solution :

    \[\cos [\pi -(B+C)]=\cos B\cos C\] Þ \[-\cos (B+C)=\cos B\cos C\] Þ \[-[\cos B\cos C-\sin B\sin C]=\cos B\cos C\] Þ \[\sin B\sin C=2\cos B\cos C\] Þ \[\tan B\tan C=2\].

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