sectheta= 5/2 হলে,  cosectheta কোনটি ? 

প্রশ্ন: \( \sec \theta = \frac{5}{2} \) হলে, \( \csc \theta \) কোনটি?

আমরা জানি, \( \sec \theta = \frac{1}{\cos \theta} \)। সুতরাং,

\( \cos \theta = \frac{1}{\sec \theta} = \frac{1}{\frac{5}{2}} = \frac{2}{5} \)

আমরা আরও জানি, \( \sin^2 \theta + \cos^2 \theta = 1 \)। সুতরাং,

\( \sin^2 \theta = 1 - \cos^2 \theta = 1 - \left(\frac{2}{5}\right)^2 = 1 - \frac{4}{25} = \frac{25 - 4}{25} = \frac{21}{25} \)

অতএব, \( \sin \theta = \sqrt{\frac{21}{25}} = \frac{\sqrt{21}}{5} \)

এখন, \( \csc \theta = \frac{1}{\sin \theta} \)। সুতরাং,

\( \csc \theta = \frac{1}{\frac{\sqrt{21}}{5}} = \frac{5}{\sqrt{21}} \)

সুতরাং, \( \csc \theta = \frac{5}{\sqrt{21}} \)। 🎉

উত্তর: \( \frac{5}{\sqrt{21}} \) ✅