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If the angle A , B and C of a triangle are in arithmetic progession and if a , b and c denote the lengths of the sides to A , B and C respectively , then the value of the expression `a/b` sin 2C + `c/a `sin 2A is

A

`1/2`

B

`(sqrt3)/2`

C

1

D

`sqrt3`

Text Solution

Verified by Experts

It is given that A, Band Care in A.P.
`therefore2B=A+C`
`rArr3B=A+B+CrArr3B=180^(@)rArrB=60^(@)`
Now,
`a/csin2C+c/asin2A`
`=(2a)/csinCcosC+(2c)/asinAcosA`
`=2(sinAcosC+cosAsinC)` [Using Sine rule]
`=2sin(A+C)=2sinB=2sin^(60)^(@)=sqrt3`
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