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Question

In a ΔABC. If tanA2,tanB2,tanC2 are in H.P, then a,b,c are in:

A
H.P
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B
G.P
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C
A.P
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D
A.G.P
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Solution

The correct option is C A.P
tanA2,tanB2,tanC2 are in H.P
{tanA2=Δs(sb)}
Δs(sa),Δs(sb),Δs(sc) are in H.P
So, s(sa)Δ,s(sb)Δ,s(sc)Δ are in A.P
2×s(sb)Δ=s(sa)Δ+s(sc)Δ
2(sb)=(sa)+(sc)
2s2b=2sac
2b=a+c
a, b, c are in A.P

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