sinθ=12/13 হলে, tanθ এর মান কত?

Explanation:

Another Explanation (5): দেওয়া আছে, \( \sin \theta = \frac{12}{13} \). 🤔 আমরা জানি, \( \sin^2 \theta + \cos^2 \theta = 1 \). 🤓 সুতরাং, \( \cos^2 \theta = 1 - \sin^2 \theta = 1 - \left(\frac{12}{13}\right)^2 = 1 - \frac{144}{169} = \frac{169 - 144}{169} = \frac{25}{169} \). 🤩 তাহলে, \( \cos \theta = \pm \sqrt{\frac{25}{169}} = \pm \frac{5}{13} \). 😎 এখন, \( \tan \theta = \frac{\sin \theta}{\cos \theta} \). 🧐 যদি \( \cos \theta = \frac{5}{13} \) হয়, তবে \( \tan \theta = \frac{\frac{12}{13}}{\frac{5}{13}} = \frac{12}{13} \times \frac{13}{5} = \frac{12}{5} \). 🥳 আবার, যদি \( \cos \theta = -\frac{5}{13} \) হয়, তবে \( \tan \theta = \frac{\frac{12}{13}}{-\frac{5}{13}} = \frac{12}{13} \times \frac{13}{-5} = -\frac{12}{5} \). 😥 অতএব, \( \tan \theta = \pm \frac{12}{5} \). 🎉