(1+cos2theta)/(sin2theta)=? 

প্রশ্ন: \(\frac{1+\cos{2\theta}}{\sin{2\theta}}=?\) 🤔

আমরা জানি, \( \cos{2\theta} = 2\cos^2{\theta} - 1 \) এবং \( \sin{2\theta} = 2\sin{\theta}\cos{\theta} \)। 🤓

সুতরাং, \( \frac{1+\cos{2\theta}}{\sin{2\theta}} = \frac{1 + (2\cos^2{\theta} - 1)}{2\sin{\theta}\cos{\theta}} \) 😊

\(= \frac{2\cos^2{\theta}}{2\sin{\theta}\cos{\theta}} \) 🤩

\(= \frac{\cos{\theta}}{\sin{\theta}} \) 😎

\(= \cot{\theta} \) 🎉

অতএব, \(\frac{1+\cos{2\theta}}{\sin{2\theta}} = \cot{\theta}\) । 🥳