tan ( tan^-1 (1/3) + tan^-1 (1/2))   এর মান কত? 

Another Explanation (5): প্রশ্ন: \(\tan (\tan^{-1} (1/3) + \tan^{-1} (1/2))\) এর মান কত? উত্তর: 1 সমাধান: ধরা যাক, \(A = \tan^{-1} (1/3)\) এবং \(B = \tan^{-1} (1/2)\) তাহলে, \(\tan A = \frac{1}{3}\) এবং \(\tan B = \frac{1}{2}\) আমরা জানি, \(\tan (A + B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}\) সুতরাং, \[ \begin{aligned} \tan (A + B) &= \frac{\frac{1}{3} + \frac{1}{2}}{1 - \left(\frac{1}{3} \times \frac{1}{2}\right)} \\ &= \frac{\frac{2}{6} + \frac{3}{6}}{1 - \frac{1}{6}} \\ &= \frac{\frac{5}{6}}{\frac{5}{6}} \\ &= 1 \end{aligned} \] অতএব, \[ \boxed{ \tan (\tan^{-1} (1/3) + \tan^{-1} (1/2)) = 1 } \]