Question

If tan(A+B)=tanA+tanB/1-tanA×tanB, tanA=1/2 and tanB=1/3 then find the value of (A+B)

Answer 1

Substituting the value of tanA and tanB in the formula
$\frac{ \tan(a) \: + \: \tan(b) }{ 1 - \tan(a) \times \tan(b) }$

We get
$\frac{ \frac{1}{2} + \frac{1}{3} }{1 - \frac{5}{6} \times \frac{1}{3} }$
Solving it we get
$\tan(a + b) = 1$
Therefore
$(a + b) = { \tan ^{ - 1} (1) }$
Hence
A+B = 45