(sin75°+sin15°)/(sin75°-sin15°)  সমান-

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, \(\frac{sin75°+sin15°}{sin75°-sin15°} = \frac{2sin(\frac{75°+15°}{2})cos(\frac{75°-15°}{2})}{2cos(\frac{75°+15°}{2})sin(\frac{75°-15°}{2})}\)

= \(\frac{sin(\frac{90°}{2})cos(\frac{60°}{2})}{cos(\frac{90°}{2})sin(\frac{60°}{2})}\)

= \(\frac{sin45°cos30°}{cos45°sin30°}\)

= \(\frac{sin45°}{cos45°} \cdot \frac{cos30°}{sin30°}\)

আমরা জানি, \(sin45° = cos45° = \frac{1}{\sqrt{2}}\) এবং \(cos30° = \frac{\sqrt{3}}{2}\), \(sin30° = \frac{1}{2}\)

সুতরাং, \(\frac{sin45°}{cos45°} \cdot \frac{cos30°}{sin30°} = 1 \cdot \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\)

= \(\frac{\sqrt{3}}{2} \cdot \frac{2}{1}\)

= \(\sqrt{3}\) 🎉

সুতরাং, \(\frac{sin75°+sin15°}{sin75°-sin15°} = \sqrt{3}\) 🥳