(sin75°-sin15°)/(sin75°+sin15°)=? 

আমরা জানি, \(sin C - sin D = 2 cos(\frac{C+D}{2}) sin(\frac{C-D}{2})\) এবং \(sin C + sin D = 2 sin(\frac{C+D}{2}) cos(\frac{C-D}{2})\).

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

\(= \frac{cos(45°) sin(30°)}{sin(45°) cos(30°)} \)

\(= \frac{sin(30°)}{cos(30°)} \), যেহেতু \(sin(45°) = cos(45°)\)

\(= tan(30°) \)

আমরা জানি, \(tan(30°) = \frac{1}{\sqrt{3}}\).

সুতরাং, \( \frac{sin75° - sin15°}{sin75° + sin15°} = \frac{1}{\sqrt{3}} \)। 🎉