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JEE Main & Advanced Mathematics Trigonometric Identities Question Bank Self Evaluation Test - Trigonometric Function

  • question_answer
    If \[A=(\cos 12{}^\circ -\cos 36{}^\circ )(\sin 96{}^\circ +\sin 24{}^\circ )\] and \[B=(\sin 60{}^\circ -\sin 12{}^\circ )(\cos 48{}^\circ -\cos 72{}^\circ ),\] then what is \[\frac{A}{B}\]equal to?

    A) -1                    

    B) \[0\]    

    C) \[1\]                 

    D) \[2\]

    Correct Answer: C

    Solution :

    Given             \[A=(\cos 12{}^\circ -\cos 36{}^\circ )(\sin 96{}^\circ +sin24{}^\circ )\] \[B=(\sin 60{}^\circ -\sin 12{}^\circ )(\cos 48{}^\circ -\cos 72{}^\circ )\] \[\frac{A}{B}=\frac{[-2\sin 24{}^\circ \sin 12{}^\circ ][2\sin 60{}^\circ \cos 36{}^\circ ]}{[2\cos 36{}^\circ \sin 24{}^\circ ][-2\sin 60{}^\circ \sin 12{}^\circ ]}\] \[\Rightarrow \,\,\frac{A}{B}=1\]


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