Question

if A and B are acute angles such that tan A = 1/3, tan B = 1/2 and tan(A+B) = (tan A+ tan B)/1-tanA.tan B

Answer 1

tan (A+B) = [tan A + tan B]/[1 - tan A*tan B] …(1)

Here tan A = 1/3 and tan B = 1/2.

So (1) becomes =[(1/3)+(1/2)/[1-(1/3)(1/2)

= (5/6)/[1–(1/6)]

= (5/6)/(5/6)

= 1 = tan 45.

Hence A + B = 45 degrees.