MSA Education BD

 $\begin{aligned} \Rightarrow & \text { AT } \\ & \tan ^{-1} x=A, \quad \tan ^{-1} y=B \\ & \Rightarrow x=\tan A \quad \Rightarrow y=\tan B \\ \therefore & \tan (A-B)=\frac{\tan A-\tan B}{1+\tan A \cdot \tan B} \\ \Rightarrow & \tan (A-B)=\frac{x-y}{1+x y} \\ \Rightarrow & A-B=\tan ^{-1} \frac{x-y}{1+x y} \\ \Rightarrow & \tan ^{-1} x-\tan ^{-1} y=\tan ^{-1} \frac{x-y}{1+x y}\end{aligned}$