Multiple choice

If ABC is a triangle and $\tan\dfrac{A}{2},\tan \dfrac{B}{2},\tan \dfrac{C}{2} $ are in H.P., then find the minimum value of $\cot B/2$.

  1. $\sqrt{3}+1$
  2. $\sqrt{3}$
  3. $\sqrt{2}$
  4. $\sqrt{2}+1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a triangle, tan(A/2), tan(B/2), tan(C/2) in H.P. implies 2/tan(B/2) = 1/tan(A/2) + 1/tan(C/2). Using the identity tan(A/2)tan(B/2) + tan(B/2)tan(C/2) + tan(C/2)tan(A/2) = 1, this simplifies to tan(B/2) = 1/sqrt(3). Thus, cot(B/2) = sqrt(3).

Keep practicing — related questions