tan^-12+tan^-13+tan^-14=θ হলে, tanθ এর মান কত? 

দেওয়া আছে, \( \tan^{-1}2 + \tan^{-1}3 + \tan^{-1}4 = \theta \)

আমরা জানি, \( \tan^{-1}x + \tan^{-1}y = \tan^{-1}\left(\frac{x+y}{1-xy}\right) \)

সুতরাং, \( \tan^{-1}2 + \tan^{-1}3 = \tan^{-1}\left(\frac{2+3}{1-(2 \times 3)}\right) \)

\( = \tan^{-1}\left(\frac{5}{1-6}\right) = \tan^{-1}\left(\frac{5}{-5}\right) = \tan^{-1}(-1) \)

এখন, \( \tan^{-1}2 + \tan^{-1}3 + \tan^{-1}4 = \tan^{-1}(-1) + \tan^{-1}4 \)

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

অতএব, \( \theta = \tan^{-1}\left(\frac{3}{5}\right) \)

সুতরাং, \( \tan\theta = \frac{3}{5} \)

অতএব, \( \tan\theta \) এর মান \( \frac{3}{5} \)। 🎉🎉