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If the angle A ,Ba n dC of a triangle ar...

If the angle `A ,Ba n dC` of a triangle are in an arithmetic propression and if `a , ba n dc` denote the lengths of the sides opposite to `A ,Ba n dC` respectively, then the value of the expression `a/csin2C+c/asin2A` is `1/2` (b) `(sqrt(3))/2` (c) `1` (d) `sqrt(3)`

A

`1/2`

B

`(sqrt(3))/2`

C

`1`

D

`sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Sicne A,B,C are in AP.
`implies2B=A+Cimplies/_B=60^(@)`
`:.a/c(2sin C cos C )+c/a(2sinn A cosA)`
`=2k(acos C+c cos AS)=2k(b)`
`2sin B`
[using `b=acosC+c cosA`]
`=sqrt(3)`
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