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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 (a) `1/2` (b) `(sqrt(3))/2` (c) `1` (d) `sqrt(3)`

A

`(1)/(2)`

B

`(sqrt3)/(2)`

C

1

D

`sqrt3`

Text Solution

Verified by Experts

The correct Answer is:
D
Since angles of `DeltaABC` are in A.P., `2B = A +C`
Also, `A + B + C = 180^(@)`
`:. B = 60^(@)`
`:. (a)/(c) sin 2C + (c)/(a) sin 2A = 2 sin A C + 2 sin C cos A = 2 sin (A +C) = 2 sin B = 2 xx (sqrt3)/(2) = sqrt3`
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