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Question

In ΔABC, if 3tanA2tanC2=1, then a,b,c are in:

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

The correct option is A A.P
We know, tanA2=(sb)(sc)s(sa)
3tanA2tanC2=3(sb)(sc)s(sa)(sa)(sb)s(sc)
3tanA2tanC2=3×sbs=3×ab+ca+b+c=1
3a3b+3c=a+b+c
2a+2c=4b
a+c=2b
Hence a,b,c are in A.P.

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