Question

If A > 0, B > 0 and A + B  = π/3, then the maximum value of tan A tan B is

(A)  1/3

(B)  1

(C)  √3

(D)  1/√3

Answer 1

Correct option  (A)  1/3

Given A + B = π/3 ⇒ B = π/3 - A

Let k = tan A tan B

Since tan A is real,

but k cannot be greater than 3, since A + B  = π /3.

Therefore, maximum value of tan A tan B is 1/3.