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Question

(cosαcosβ)2+(sinαsinβ)2=4sin2{(αβ)/2}

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Solution

(cosαcosβ)2+(sinαsinβ)2
=cos2α+cos2β2cosαcosβ+sin2α+sin2β2sinαsinβ
=1+12(cosαcosβ+sinαsinβ)
=2(1cos(αβ))
=2×2sin2(αβ2)
=4sin2(αβ2)

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