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

  • question_answer
    \[\sin {{163}^{o}}\cos {{347}^{o}}+\sin {{73}^{o}}\sin {{167}^{o}}=\] [MP PET 2000]

    A) 0

    B) 1/2

    C) 1

    D) None of these

    Correct Answer: B

    Solution :

    \[\sin {{163}^{o}}\cos {{347}^{o}}+\sin {{73}^{o}}\sin {{167}^{o}}\] \[=\sin ({{180}^{o}}-{{17}^{o}})\cos ({{360}^{o}}-{{13}^{o}})+\cos ({{90}^{o}}-{{17}^{o}})\]\[\sin ({{180}^{o}}-{{13}^{o}})\] \[=\sin {{17}^{o}}\cos {{13}^{o}}+\cos {{17}^{o}}\sin {{13}^{o}}=\sin {{30}^{o}}=1/2\].


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