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

  • question_answer
    If \[\sin A=\sin B\]and \[\cos A=\cos B,\]then [EAMCET 1994]

    A) \[\sin \frac{A-B}{2}=0\]

    B) \[\sin \frac{A+B}{2}=0\]

    C) \[\cos \frac{A-B}{2}=0\]

    D) \[\cos (A+B)=0\]

    Correct Answer: A

    Solution :

    We have \[\sin A=\sin B\] and \[\cos A=\cos B\] \[\frac{\sin A}{\sin B}=\frac{\cos A}{\cos B}\,\Rightarrow \,\,\sin A\,\cos B-\cos A\,\sin B=0\] \[\Rightarrow \,\,\sin \,(A-B)=0\] Hence, \[\sin \,\left( \frac{A-B}{2} \right)=0.\]


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