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)   √3/2

(c)   1

(d)   √3

Answer 1

correct option (D)   √3.

Given that angles of the triangle are in AP ⇒ 2∠B = ∠A + ∠C and ∠A + ∠B + ∠C = π

⇒ ∠B =  π/3

Hence,   2 sinB = 2sin π/3 = √3.