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

  • question_answer
    \[\sin 12{}^\circ \sin 48{}^\circ \sin 54{}^\circ =\] [IIT 1982; Kerala (Engg.) 2001]

    A) 1/16

    B) 1/32

    C) 1/8

    D) 1/4

    Correct Answer: C

    Solution :

     \[\sin \,{{12}^{o}}\,\sin \,{{48}^{o}}\,\sin \,{{54}^{o}}=\frac{1}{2}\,\left\{ \cos {{36}^{o}}-\cos {{60}^{o}} \right\}\,\cos \,{{36}^{o}}\] \[=\frac{1}{2}\,\left[ \frac{\sqrt{5}+1}{4}-\frac{1}{2} \right]\,\left[ \frac{\sqrt{5}+1}{4} \right]=\frac{1}{2}\,\left[ \frac{\sqrt{5}-1}{4} \right]\,\left[ \frac{\sqrt{5}+1}{4} \right]\] \[=\frac{5-1}{32}=\frac{4}{32}=\frac{1}{8}\].


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