tan 70° tan 30° tan 20° =?

Explanation:

Another Explanation (5): দেওয়া আছে, \( \tan 70^\circ \tan 30^\circ \tan 20^\circ \) এর মান নির্ণয় করতে হবে। আমরা জানি, \( \tan 30^\circ = \frac{1}{\sqrt{3}} \) সুতরাং, \( \tan 70^\circ \tan 30^\circ \tan 20^\circ = \tan 70^\circ \cdot \frac{1}{\sqrt{3}} \cdot \tan 20^\circ \) \( = \frac{1}{\sqrt{3}} \cdot \tan 70^\circ \tan 20^\circ \) আমরা আরও জানি, \( \tan (A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B} \) এখন, \( \tan (70^\circ + 20^\circ) = \tan 90^\circ = \infty \) সুতরাং, \( 1 - \tan 70^\circ \tan 20^\circ = 0 \) অতএব, \( \tan 70^\circ \tan 20^\circ = 1 \) সুতরাং, \( \tan 70^\circ \tan 30^\circ \tan 20^\circ = \frac{1}{\sqrt{3}} \cdot 1 = \frac{1}{\sqrt{3}} \) 🎉🎉 অতএব, \( \tan 70^\circ \tan 30^\circ \tan 20^\circ = \frac{1}{\sqrt{3}} \) 😎