MCQ
${\tan ^{ - 1}}\left( {\frac{x}{y}} \right) - {\tan ^{ - 1}}\,\left( {\frac{{x - y}}{{x + y}}} \right) = . . .$
- A$\frac{\pi }{2}$
- B$\frac{\pi }{3}$
- ✓$\frac{\pi }{4}$
- D$\frac{\pi }{4}$ અથવા $ - \frac{{3\pi }}{4}$
$ = {\tan ^{ - 1}}\frac{x}{y} - \left( {{{\tan }^{ - 1}}1 - {{\tan }^{ - 1}}\frac{y}{x}} \right)$
$ = {\tan ^{ - 1}}\frac{x}{y} + {\tan ^{ - 1}}\frac{y}{x} - \frac{\pi }{4}$
$ = {\tan ^{ - 1}}\frac{x}{y} + {\cot ^{ - 1}}\frac{x}{y} - \frac{\pi }{4} = \frac{\pi }{2} - \frac{\pi }{4} = \frac{\pi }{4}$.
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