Question

prove that
tan-1(1/2)+tan-1(1/3)=(π/4)​

Answer 1

$\tan^{ - 1} \left(\frac{1}{2}\right ) + \tan^{ - 1}\left(\frac{1}{3} \right) = \tan^{ - 1} \left(\frac{ \frac{1}{2} + \frac{1}{3} }{1- \frac{1}{2} \times \frac{1}{3} }\right) \\ = \tan^{ - 1} \left(\frac{ \frac{5}{6}}{1- \frac{1}{6} }\right) \\ = \tan^{ - 1} \left(\frac{ \frac{5}{6}}{\frac{5}{6} }\right) \\ = \tan^{ - 1} (1) \\ = \frac{\pi}{4}$

Hence proved