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Question

If sides of a triangle are in A.P. and the greatest angle is two times the smallest angle in the trian then cosine of least angle is

A
3/8
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B
2/3
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C
1/8
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D
3/4
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Solution

The correct option is D 3/4
Let angles of triangle be A,B,C
with corresponding sides a,b,c.
Let A=θ,B=n3θ,C=θ
2b=a+c
=sinCc=sinCc=sinAa=k
b=sinBk,c=sinCk,a=sinAk
2sinBk=sinAk+sinCk
=2sin3θ=Sinθ+sin2θ
=2(3sinθ4sin3θ)=sinθ(1+2cosθ)
=68(1cos2θ)=1+2cosθ
cosθ=34,12
But cosθ12
cosθ=34

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