\(tan^{-1}(\frac xy)-tan^{-1}(\frac{x-y}{x+y})\)
\(=tan^{-1}\left(\cfrac{\frac xy-\frac{x-y}{x+y}}{1+\frac xy.\frac{x-y}{x+y}}\right)\) \([Here \frac xy.\frac{x-y}{x+y}>-1]\)
\(=tan^{-1}(\frac{x^2+xy-xy+y^2}{y(x+y)}\times\)\(\frac{y(x+y)}{xy+y^2+x^2-xy})\)
\(=tan^{-1}(\frac{x^2+y^2}{x^2+y^2})\)
\(=tan^{-1}(1)=\frac{\pi}4\)