tan^-1(p)= sin^-1(2/3)   হলে p এর মান কত ?  

Explanation:

Another Explanation (5): bài toán: \(tan^{-1}(p) = sin^{-1}(\frac{2}{3})\) হলে \(p\) এর মান নির্ণয় করো। সমাধান: মনে করি, \(sin^{-1}(\frac{2}{3}) = \theta\) সুতরাং, \(sin(\theta) = \frac{2}{3}\) আমরা জানি, \(sin^2(\theta) + cos^2(\theta) = 1\) সুতরাং, \(cos^2(\theta) = 1 - sin^2(\theta) = 1 - (\frac{2}{3})^2 = 1 - \frac{4}{9} = \frac{5}{9}\) সুতরাং, \(cos(\theta) = \sqrt{\frac{5}{9}} = \frac{\sqrt{5}}{3}\) এখন, \(tan(\theta) = \frac{sin(\theta)}{cos(\theta)} = \frac{\frac{2}{3}}{\frac{\sqrt{5}}{3}} = \frac{2}{\sqrt{5}}\) যেহেতু, \(tan^{-1}(p) = \theta\) সুতরাং, \(tan(\theta) = p\) অতএব, \(p = \frac{2}{\sqrt{5}}\) 🥳