(sin75° + sin15°)/(sin75° - sin15°)  এর মান-

Explanation:

Another Explanation (5): bài toán: \(\frac{sin75° + sin15°}{sin75° - sin15°}\) = ? আমরা জানি, sinC + sinD = \(2sin\frac{C+D}{2}cos\frac{C-D}{2}\) এবং sinC - sinD = \(2cos\frac{C+D}{2}sin\frac{C-D}{2}\) অতএব, \(\frac{sin75° + sin15°}{sin75° - sin15°} = \frac{2sin\frac{75°+15°}{2}cos\frac{75°-15°}{2}}{2cos\frac{75°+15°}{2}sin\frac{75°-15°}{2}}\) = \(\frac{sin\frac{90°}{2}cos\frac{60°}{2}}{cos\frac{90°}{2}sin\frac{60°}{2}}\) = \(\frac{sin45°cos30°}{cos45°sin30°}\) আমরা জানি, sin45° = cos45° = \(\frac{1}{\sqrt{2}}\) , sin30° = \(\frac{1}{2}\) এবং cos30° = \(\frac{\sqrt{3}}{2}\) সুতরাং, \(\frac{sin45°cos30°}{cos45°sin30°} = \frac{\frac{1}{\sqrt{2}} \cdot \frac{\sqrt{3}}{2}}{\frac{1}{\sqrt{2}} \cdot \frac{1}{2}}\) = \(\frac{\sqrt{3}/2}{1/2}\) = \(\sqrt{3}\) ∴ \(\frac{sin75° + sin15°}{sin75° - sin15°} = \sqrt{3}\) উত্তর: √3 🎉🥳