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Question

Prove that (cos2 48sin2 12)=(5+1)8


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    Solution

    We have

    LHS = (cos2 48sin2 12)

    =12(2cos2 482sin2 12)

    =12(1+cos96)(1cos24)

    [2cos2θ=(1+cos 2θ) and 2sin2 θ=(1cos 2θ)]

    =12(cos96 +cos24)

    =12 [2 cos(96+242)cos(96242)]

    =12 ×2cos 60 36 =12× (5+1)4 [ cos 36=(5+1)4]

    = (5+1)8=RHS


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