(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 🎉🥳
