7sin^2theta +3cos^2theta=4 হলে  sectheta  এর মান কোনটি?

Explanation:

Another Explanation (5): দেওয়া আছে, \(7\sin^2\theta + 3\cos^2\theta = 4\) আমরা জানি, \(\sin^2\theta + \cos^2\theta = 1\) তাহলে, \(\sin^2\theta = 1 - \cos^2\theta\) এখন, \(7(1-\cos^2\theta) + 3\cos^2\theta = 4\) \(\implies 7 - 7\cos^2\theta + 3\cos^2\theta = 4\) \(\implies 7 - 4\cos^2\theta = 4\) \(\implies 4\cos^2\theta = 7-4\) \(\implies 4\cos^2\theta = 3\) \(\implies \cos^2\theta = \frac{3}{4}\) \(\implies \cos\theta = \pm\sqrt{\frac{3}{4}}\) \(\implies \cos\theta = \pm\frac{\sqrt{3}}{2}\) সুতরাং, \(\sec\theta = \frac{1}{\cos\theta} = \pm\frac{2}{\sqrt{3}}\) 🥳 যেহেতু উত্তরে \( \frac{2}{\sqrt{3}} \) আছে, তাই সেটাই উত্তর। উত্তর: \(\frac{2}{\sqrt{3}}\) ✅