যদি 3sec⁴θ +8=10 sec²θ  হয়, তবে tan θ এর মান হবে-

Explanation:

Another Explanation (5): দেওয়া আছে, \(3\sec^4\theta + 8 = 10\sec^2\theta\) ধরি, \(\sec^2\theta = x\) তাহলে, \(3x^2 + 8 = 10x\) \(\implies 3x^2 - 10x + 8 = 0\) \(\implies 3x^2 - 6x - 4x + 8 = 0\) \(\implies 3x(x - 2) - 4(x - 2) = 0\) \(\implies (x - 2)(3x - 4) = 0\) সুতরাং, \(x = 2\) অথবা \(x = \frac{4}{3}\) যদি \(x = 2\) হয়, তবে \(\sec^2\theta = 2\) \(\implies 1 + \tan^2\theta = 2\) \(\implies \tan^2\theta = 1\) \(\implies \tan\theta = \pm 1\) আবার, যদি \(x = \frac{4}{3}\) হয়, তবে \(\sec^2\theta = \frac{4}{3}\) \(\implies 1 + \tan^2\theta = \frac{4}{3}\) \(\implies \tan^2\theta = \frac{4}{3} - 1\) \(\implies \tan^2\theta = \frac{1}{3}\) \(\implies \tan\theta = \pm \frac{1}{\sqrt{3}}\) অতএব, \(\tan\theta\) এর মান \(\pm \frac{1}{\sqrt{3}}\) অথবা \(\pm 1\)। 🎉🎉