sin 11 theta/4 sin theta /4 + sin 7 theta /4 sin 3 theta/4 sin 2 theta sin theta

Dear student
sin11θ4sinθ4+sin7θ4sin3θ4=cos11θ4-θ4-cos11θ4+θ42+cos7θ4-3θ4-cos7θ4+3θ42 sinx siny=cos(x-y)-cos(x+y)2=cos5θ2-cos3θ2+cosθ-cos5θ22=cosθ-cos3θ2=sinθ+3θ2sin3θ-θ2           cosx-cosy=2sinx+y2siny-x2=sin2θ.sinθ
Regards

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