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Question

If sinαsinβ=1/3 and cosβcosα=1/2, then cotα+β2=k3. Find the value of k.

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Solution

sinαsinβ=132cos(α+β2)sin(αβ2)=13 ...(1)
cosβcosα=122sin(α+β2)sin(αβ2)=12 ...(2)
Dividing equation(1) by equation(2) we get
cot(α+β2)=1312=23k=2

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