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Question

(cosα+cosβ)2+(sinα+sinβ)2=bcos2(αβ2) Find b

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Solution

L.H.S. =(cosα+cosβ)2+(sinα+sinβ)2
={2cos(α+β2)cos(αβ2)}2+{2sin(α+β2)cos(αβ2)}2
=4cos2(αβ2){cos2α+β2+sin2α+β2}=4cos2(αβ2)
Ans: 4

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