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If the angles A, B and C of a triangle a...

If the angles A, B and C of a triangle are in an arithmetic progression and if a, b and c denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression `(a)/(c) 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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