7sin2θ+ 3cos2θ = 4 হলে tanθ এর মান কত ?
7sin2θ+ 3cos2θ = 4 হলে tanθ এর মান কত ?
সঠিক উত্তরঃ
A.
1 /√ 3
Explanation:
![](\"https://testmozusercontent.com/ugc/2023-09-18/2e5bb4b7-d7c8-4939-beed-889695beae65-image.png\")
Another Explanation (5): ```html
দেওয়া আছে, \( 7\sin^2\theta + 3\cos^2\theta = 4 \) 🤔
আমরা জানি, \( \sin^2\theta + \cos^2\theta = 1 \) 🤓
তাহলে, \( 7\sin^2\theta + 3\cos^2\theta = 4 \) কে লেখা যায়:
\( 4\sin^2\theta + 3(\sin^2\theta + \cos^2\theta) = 4 \) 🧐
\( 4\sin^2\theta + 3 = 4 \) 🤩
\( 4\sin^2\theta = 1 \) 🥳
\( \sin^2\theta = \frac{1}{4} \) 😲
\( \sin\theta = \pm \frac{1}{2} \) 😮
\( 4\sin^2\theta + 3(\sin^2\theta + \cos^2\theta) = 4 \) 🧐
\( 4\sin^2\theta + 3 = 4 \) 🤩
\( 4\sin^2\theta = 1 \) 🥳
\( \sin^2\theta = \frac{1}{4} \) 😲
\( \sin\theta = \pm \frac{1}{2} \) 😮
এখন, \( \cos^2\theta = 1 - \sin^2\theta = 1 - \frac{1}{4} = \frac{3}{4} \) 🤗
সুতরাং, \( \cos\theta = \pm \frac{\sqrt{3}}{2} \) 🤯
সুতরাং, \( \cos\theta = \pm \frac{\sqrt{3}}{2} \) 🤯
অতএব, \( \tan\theta = \frac{\sin\theta}{\cos\theta} = \frac{\pm \frac{1}{2}}{\pm \frac{\sqrt{3}}{2}} = \frac{1}{\sqrt{3}} \) অথবা \( -\frac{1}{\sqrt{3}} \) হতে পারে।
সাধারণভাবে, \( \tan\theta = \frac{1}{\sqrt{3}} \) 😎
```