JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Trigonometrical ratios of sum and difference of two and three angles

  • question_answer
    \[\cos \frac{\pi }{7}\cos \frac{2\pi }{7}\cos \frac{4\pi }{7}=\] [MP PET 1998]

    A) 0

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

    C) \[\frac{1}{4}\]

    D) \[-\frac{1}{8}\]

    Correct Answer: D

    Solution :

    \[\cos \frac{\pi }{7}.\cos \frac{2\pi }{7}.\cos \frac{4\pi }{7}=\left[ \frac{\sin \left( {{2}^{3}}.\frac{\pi }{7} \right)}{{{2}^{3}}\sin \left( \frac{\pi }{7} \right)} \right]=\frac{\sin \frac{8\pi }{7}}{8\sin \frac{\pi }{7}}=-\frac{1}{8}\].


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