(2tantheta)/(1+tan^2 theta=?  

🤔 প্রশ্ন: \(\frac{2\tan\theta}{1+\tan^2\theta} = ? \)

💡 আমরা জানি, \(\tan\theta = \frac{\sin\theta}{\cos\theta}\)

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

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

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

অতএব, = \(\frac{\frac{2\sin\theta}{\cos\theta}}{\frac{1}{\cos^2\theta}}\)

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

= \(2\sin\theta \cos\theta\)

✅ উত্তর: \(2\sin\theta \cos\theta\)