Question

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`

Answer 1

Correct Answer - 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`