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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 \[\cos (A+B)=\alpha \cos A\cos B+\beta \sin A\sin B,\]then \[(\alpha ,\beta )\]=  [MP PET 1992]

    A) (-1, -1)

    B) (- 1, 1)

    C) (1, -1)

    D) (1, 1)

    Correct Answer: C

    Solution :

    Given \[\cos \,(A+B)=\alpha \,\cos A\,\cos B+\beta \,\sin A\,\sin B\] But \[\cos \,(A+B)=\cos \,A\,\cos B-\sin A\,\sin \,B\] \[\Rightarrow \,\,\alpha =1,\,\,\beta =-1.\]


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