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Question

If sin4α+4cos4β+2=42 sinα cosβ;α,βϵ[0,π], then cos(α+β)cos(α+β) is equal to :

A
0
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B
2
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C
1
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D
2
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Solution

The correct option is C 2
A.M. G.M.
sin4α+4cos4β+1+14(sin4α.4.cos4β.1.1)14
A.M.=G.M.sin4α=1=4cos4β
sinα=1,cosβ=±12
sinβ=12 as βϵ[0,π]
cos(α+β)cos(αβ)=2sinαsinβ
= 2

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