sectheta=5/2   হলে cosectheta  কোনটি? 

Explanation:

Another Explanation (5): দেওয়া আছে, \( \sec \theta = \frac{5}{2} \) আমরা জানি, \( \sec^2 \theta = 1 + \tan^2 \theta \) সুতরাং, \( \tan^2 \theta = \sec^2 \theta - 1 \) \( \tan^2 \theta = \left(\frac{5}{2}\right)^2 - 1 = \frac{25}{4} - 1 = \frac{25-4}{4} = \frac{21}{4} \) তাহলে, \( \tan \theta = \pm \frac{\sqrt{21}}{2} \) আমরা জানি, \( \cot \theta = \frac{1}{\tan \theta} \) সুতরাং, \( \cot \theta = \pm \frac{2}{\sqrt{21}} \) আবার, \( \csc^2 \theta = 1 + \cot^2 \theta \) \( \csc^2 \theta = 1 + \left(\pm \frac{2}{\sqrt{21}}\right)^2 = 1 + \frac{4}{21} = \frac{21+4}{21} = \frac{25}{21} \) অতএব, \( \csc \theta = \pm \sqrt{\frac{25}{21}} = \pm \frac{5}{\sqrt{21}} \) যেহেতু উত্তরে \( \frac{5}{\sqrt{21}} \) আছে, তাই \( \csc \theta = \frac{5}{\sqrt{21}} \) হবে। \(\therefore\) \( \csc \theta = \frac{5}{\sqrt{21}} \) 🎉