MCQ
$\tan ^{-1}\left(\frac{x}{y}\right)-\tan ^{-1} \frac{x-y}{x+y}$ $=$ .......... .
- A$\frac{\pi}{4}$
- B$\frac{-3 \pi}{4}$
- C$\frac{\pi}{2}$
- D$\frac{\pi}{3}$
$=\tan ^{-1}\left[\frac{\frac{x}{y}-\frac{x-y}{x+y}}{1+\left(\frac{x}{y}\right)\left(\frac{x-y}{x+y}\right)}\right]$
$=\tan ^{-1}\left[\frac{\frac{x(x+y)-y(x-y)}{y(x+y)}}{\frac{y(x+y)+x(x-y)}{y(x+y)}}\right]$
$=\tan ^{-1}\left(\frac{x^{2}+x y-x y+y^{2}}{x y+y^{2}+x^{2}-x y}\right)$
$=\tan ^{-1}\left(\frac{x^{2}+y^{2}}{x^{2}+y^{2}}\right)=\tan ^{-1} 1=\frac{\pi}{4}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.