7sin²θ+3cos²θ=4 হলে,tanθ এর মান কত?

দেওয়া আছে, \(7\sin^2\theta + 3\cos^2\theta = 4\)

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

সুতরাং, \(7\sin^2\theta + 3\cos^2\theta = 4\) কে লেখা যায়,

\(4\sin^2\theta + 3(\sin^2\theta + \cos^2\theta) = 4\)

\(\implies 4\sin^2\theta + 3 \times 1 = 4\)

\(\implies 4\sin^2\theta = 4 - 3\)

\(\implies 4\sin^2\theta = 1\)

\(\implies \sin^2\theta = \frac{1}{4}\)

\(\implies \sin\theta = \pm\frac{1}{2}\) 😮

এখন, \(\cos^2\theta = 1 - \sin^2\theta = 1 - \frac{1}{4} = \frac{3}{4}\)

\(\implies \cos\theta = \pm\frac{\sqrt{3}}{2}\) 😎

অতএব, \(\tan\theta = \frac{\sin\theta}{\cos\theta} = \frac{\pm\frac{1}{2}}{\pm\frac{\sqrt{3}}{2}} = \pm\frac{1}{\sqrt{3}}\) 🤔

সুতরাং, \(\tan\theta = \pm\frac{1}{\sqrt{3}}\) 🎉