Question

A positive acute angle is divided into two parts whose tangents are 1/2 and 1/3,Show that the angle is pi/4.

Answer 1

well you can use the sum of 2 angles for tan

\[\tan(A + B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A)\tan(B)}\]

let tan(A) = 1/2 and tan(B) = 1/3

substitute and you should be able to show

tan(A + B) = 1

so A + B = pi/4