Question

If the angles A, B, C are the solutions of the equation tan³x – 3k.tan²x – 3tanx + k = 0, then the △ABC is

(a) isosceles

(b) equilateral

(c) acute angled

(d) None of these

Answer 1

Correct option is (d) None of these

tanA, tanB, tanC are roots of the given equation

∴ tanA + tanB + tanC = 3k, tanAtanB + tanBtanC + tanCtanA = –3 and tanA.tanB.tanC = – k

But tanA + tanB + tanC = tanA tanB tanC

⇒ 3k = – k ⇒ 4k = 0 gives k= 0

∴ tanAtanBtanC = 0

⇒ tanA = 0 or tanB = 0 or tanC = 0 which is not possible