If tanA=1/2 and tanB=1/3,Then Prove That: A+B=45Degree.

We know that, Tan(A+B) = (TanA + TanB) / (1 - TanA.TanB)

Therefore,

tan(A + B) = { (1/2) + (1/3) } / { 1 - (1/2)(1/3) }                          {Replacing the values of tanA and tanB}

 tan(A + B) = { ( 3+2 ) / ( 6 ) } / { ( 6-1 ) / (6) }

 tan(A + B) = (5/6) / (5/6)

 tan(A + B) = 1

 tan(A + B) = tan (45°)                                                {since, tan 45° = 1}

 A + B = 45°

Hence, proved!