Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

From the given equation, we have

$$\begin{array}{rlr}& \tan (A+B)+\tan (A-B)=4& \tan (A+B)\tan (A-B)=1\end{array}$$

From (1) and (2) we get

$$\begin{array}{rlr}& \tan [A+B+A-B]=\tan \pi /2& \Rightarrow 2A=\pi /2\Rightarrow A=\pi /4\end{array}$$

and from (1) we get

$$\begin{array}{rlr}& \frac{1+\tan B}{1-\tan B}+\frac{1-\tan B}{1+\tan B}=4& \Rightarrow \cos 2B=1/2\Rightarrow B=\pi /6\end{array}$$