যদি 5tanθ=4 হয়, তাহলে  (5sintheta-3costheta)/(sintheta+2costheta) =?

Explanation:

Another Explanation (5): যদি \(5\tan\theta = 4\) হয়, তাহলে \(\frac{5\sin\theta - 3\cos\theta}{\sin\theta + 2\cos\theta}\) এর মান নির্ণয় করতে হবে। আমরা জানি, \(\tan\theta = \frac{\sin\theta}{\cos\theta}\)। সুতরাং, \(5 \frac{\sin\theta}{\cos\theta} = 4\) অতএব, \(\sin\theta = \frac{4}{5}\cos\theta\) এখন, প্রদত্ত রাশিমালাটি হলো: \[ \frac{5\sin\theta - 3\cos\theta}{\sin\theta + 2\cos\theta} \] \(\sin\theta\) এর মান বসিয়ে পাই, \[ \frac{5(\frac{4}{5}\cos\theta) - 3\cos\theta}{\frac{4}{5}\cos\theta + 2\cos\theta} \] \[ = \frac{4\cos\theta - 3\cos\theta}{\frac{4}{5}\cos\theta + \frac{10}{5}\cos\theta} \] \[ = \frac{\cos\theta}{\frac{14}{5}\cos\theta} \] \[ = \frac{1}{\frac{14}{5}} \] \[ = \frac{5}{14} \] সুতরাং, \(\frac{5\sin\theta - 3\cos\theta}{\sin\theta + 2\cos\theta} = \frac{5}{14}\) 🎉