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If A,B,C, are the angles of a triangle such that `cotA/2=3tanC/2,` then `sinA ,sinB ,sinC` are in `AdotPdot` (b) `GdotPdot` (c) `HdotPdot` (d) none of these

A

AP

B

GP

C

HP

D

none of these.

Text Solution

Verified by Experts

The correct Answer is:
A
Given `cot((A)/(2))cot((C)/(2))=3`
`rArr (cos((A)/(2))cos((C)/(2)))/(sin((A)/(2))sin((C)/(2)))=3`
`rArr(cos((A-C)/(2)))/(cos((A+C)/(2)))=2`
`rArr 2sinB=sinA+sinC`
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