Question

If A and B are acute angles such that $\tan A=\frac{1}{2},\tan B=\frac{1}{3}\mathrm{and}\tan \left(A+B\right)=\frac{\tan A+\tan B}{1-\tan A\tan B}$, find A + B.

Answer 1

Given:

…… (1)

…… (2)

…… (3)

Now by substituting the value of and from equation (1) and (2) in equation (3)

We get,

Therefore,

…… (3)

Now we know that

…… (4)

Now by comparing equation (3) and (4)

We get,