Cosθ=12/13 হলে Tan2θ সমান কত?

Explanation:

Another Explanation (5): দেওয়া আছে, \( \cos\theta = \frac{12}{13} \) 🤔 আমরা জানি, \( \sin^2\theta + \cos^2\theta = 1 \) 😊 তাহলে, \( \sin^2\theta = 1 - \cos^2\theta \) \( \sin^2\theta = 1 - \left(\frac{12}{13}\right)^2 \) \( \sin^2\theta = 1 - \frac{144}{169} \) \( \sin^2\theta = \frac{169 - 144}{169} \) \( \sin^2\theta = \frac{25}{169} \) সুতরাং, \( \sin\theta = \pm\frac{5}{13} \) 🤩 এখন, \( \tan\theta = \frac{\sin\theta}{\cos\theta} \) \( \tan\theta = \frac{\pm\frac{5}{13}}{\frac{12}{13}} \) \( \tan\theta = \pm\frac{5}{12} \) 🥳 আমরা জানি, \( \tan2\theta = \frac{2\tan\theta}{1 - \tan^2\theta} \) 🤓 তাহলে, \( \tan2\theta = \frac{2\left(\pm\frac{5}{12}\right)}{1 - \left(\pm\frac{5}{12}\right)^2} \) \( \tan2\theta = \frac{\pm\frac{5}{6}}{1 - \frac{25}{144}} \) \( \tan2\theta = \frac{\pm\frac{5}{6}}{\frac{144 - 25}{144}} \) \( \tan2\theta = \frac{\pm\frac{5}{6}}{\frac{119}{144}} \) \( \tan2\theta = \pm\frac{5}{6} \times \frac{144}{119} \) \( \tan2\theta = \pm\frac{5 \times 24}{119} \) \( \tan2\theta = \pm\frac{120}{119} \) 😎 অতএব, \( \tan2\theta = \pm\frac{120}{119} \) 🎉