KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    \[\sin 47{}^\circ +\sin 61{}^\circ -\sin 11{}^\circ -\sin 25{}^\circ \] is equal to

    A) \[\sin 36{}^\circ \]

    B) \[\cos 36{}^\circ \]

    C) \[\sin 7{}^\circ \]

    D) \[\cos 7{}^\circ \]

    Correct Answer: D

    Solution :

    The given expression is equal to
    \[(\sin 47{}^\circ +\sin 61{}^\circ )-(sin11{}^\circ +sin25{}^\circ )\]\[=2\sin 54{}^\circ \cos 7{}^\circ -2\sin 18{}^\circ \cos 7{}^\circ \]\[=2\cos 7{}^\circ \,(\sin 54{}^\circ -\sin 18{}^\circ )\]
    \[=2\,\cos 7{}^\circ \left[ \frac{\sqrt{5}+1}{4}-\frac{\sqrt{5}-1}{4} \right]=\cos 7{}^\circ \]

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