Question

If A and B ae acute angles such that tan A =1/2 , tan B =1/3 and tan
(A + B) =tanA+tanB/1-tanAtanB, find A + B.

Answer 1

Answer:

ans should be 45°

check it and tell me if you have any doubts regarding the ans

Answer 2

A + B = 45°

Step-by-step explanation:

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

Find: A+ B

Solution:  

 tan A = 1/2

 tan B = 1/3

 tan (A + B) = tanA + tanB / 1-tanAtanB

 RHS = tanA + tanB / 1-tanAtanB

     = (1/2 + 1/3) / (1 - 1/2*1/3)

     = 5/6 / (1 - 1/6)

     = 5/6 / (5/6)

     = 1

  tan (A + B) = 1

  tan 45° = 1

 Therefore A + B = 45°