Question

Let m = (tan^-1 1 + tan^-1 2 + tan^-1 3)/(cot^-1 1 + cot^-1 2 + cot^-1 3), then prove that (m + 2)^{m + 1} = 64.

Answer 1

Given,m = (tan^-1 1 + tan^-1 2 + tan^-1 3)/(cot^-1 1 + cot^-1 2 + cot^-1 3)

= π/(π/2) = 2

Hence, the value of

(m + 2)^{m + 1} = (2 + 2)³ = 4³ = 64