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Question

If sinα,sinβ,sinγ are in A.P. and cosα,cosβ,cosγ are in G.P., then cos2α+cos2γ4cosαcosγ1+sinαsinγ is equal to

A
2
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B
1
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C
0
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D
2
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Solution

The correct option is D 2

Assume y=cos2α+cos2γ4cosα.cosγ1sinα.sinγ
since, sinα,sinβ,sinγ are in A.P 2sinβ=sinα+sinγ
squaring, 4sin2β=sin2α+sin2γ+2sinα.sinγ=2(cos2α+cos2γ)+2sinα.sinγ
and cosα,cosβ,cosγ are in G.P cos2β=cosα.cosγ
Using this equation,
y=cos2α+cos2γ4cosα.cosγ1+sinα.sinγ
=2+2sinα.sinγ4sin2β4cos2β1+sinα.sinγ
=2+2sinα.sinγ1+sinα.sinγ=2


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