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Question

If sinα,sinβ,sinγ are in A.P and cosα,cosβ,cosγ are in G.P then cos2α+cos2γ4cosαcosγ1sinαsinγ

A
-2
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B
-1
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C
\N
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D
2
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Solution

The correct option is A -2
From the given conditions we have 2 sinβ=sinα+sinγ(i),cos2β=cosαcosγ(ii)
Squaring (i), 4sin2β=sin2α+sin2γ+2sinαsinγ
Using (ii), 4(1cosαcosγ)=1cos2α+1cos2γ+2sinαsinγ
cos2α+cos2γ4cosαcosγ=2(sinαsinγ1)cos2α+cos2γ4cosαcosγ1sinαsinγ=2

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