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 - tan A tan B)`, show that A + B = 45°.

Answer 1

Given:

tan A = `1/3 and tan B = 1/2`

tan (A+B) = `(tan A + tan B)/(1- tan A  tan B)`

On substituting these values in RHS of the expression, we get:

`(tan A + tan B )/(1- tan A tan B) = ((1/3 +1/2))/((1-1/3xx1/3)` =`((5/6))/(1-1/6) = ((5/6))/((5/6))=1`

⇒ tan (A + B) = 1= tan `45^0`      [ ∵ tan 450 =1]

∴ A+B = 45⁰