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

  • question_answer
    If \[\frac{\cos A}{\sin B\sin C}+\frac{\cos B}{\sin C\sin A}+\frac{\cos C}{\sin A\sin B}=\]then \[32\sin \left( \frac{A}{2} \right)\sin \left( \frac{5A}{2} \right)=\] [DCE 1996]

    A) 7

    B) 8

    C) 11

    D) None of these

    Correct Answer: C

    Solution :

    \[32\sin \frac{A}{2}\sin \frac{5A}{2}=16(\cos 2A-\cos 3A)\] \[=16(2{{\cos }^{2}}A-1-4{{\cos }^{3}}A+3\cos A)\] \[=16\left( 2\times \frac{9}{16}-1-4\times \frac{27}{64}+3\times \frac{3}{4} \right)=11\].

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