cosec theta+cottheta=√3 হলে,  theta এর মান কত?

দেওয়া আছে, \(cosec \theta + cot \theta = \sqrt{3}\)

আমরা জানি, \(cosec^2 \theta - cot^2 \theta = 1\)

সুতরাং, \((cosec \theta + cot \theta)(cosec \theta - cot \theta) = 1\)

\(\Rightarrow \sqrt{3}(cosec \theta - cot \theta) = 1\)

\(\Rightarrow cosec \theta - cot \theta = \frac{1}{\sqrt{3}}\)

এখন, \(cosec \theta + cot \theta = \sqrt{3}\) এবং \(cosec \theta - cot \theta = \frac{1}{\sqrt{3}}\) যোগ করে পাই,

\(2cosec \theta = \sqrt{3} + \frac{1}{\sqrt{3}} = \frac{3+1}{\sqrt{3}} = \frac{4}{\sqrt{3}}\)

\(\Rightarrow cosec \theta = \frac{2}{\sqrt{3}}\)

\(\Rightarrow sin \theta = \frac{\sqrt{3}}{2}\)

আমরা জানি, \(sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}\)

অতএব, \(\theta = \frac{\pi}{3}\) 🥳