(cos15°+sin15°)/(cos15°-sin15°)=? 

Explanation:

Another Explanation (5):

প্রশ্ন: \(\frac{\cos 15^\circ + \sin 15^\circ}{\cos 15^\circ - \sin 15^\circ} = ?\) 🤔

সমাধান:

আমরা জানি, \(\tan \theta = \frac{\sin \theta}{\cos \theta}\).

লব ও হরকে \(\cos 15^\circ\) দিয়ে ভাগ করে পাই,

\[ \frac{\cos 15^\circ + \sin 15^\circ}{\cos 15^\circ - \sin 15^\circ} = \frac{\frac{\cos 15^\circ}{\cos 15^\circ} + \frac{\sin 15^\circ}{\cos 15^\circ}}{\frac{\cos 15^\circ}{\cos 15^\circ} - \frac{\sin 15^\circ}{\cos 15^\circ}} \] \[ = \frac{1 + \tan 15^\circ}{1 - \tan 15^\circ} \]

আমরা জানি, \(\tan (A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}\).

এখানে, \(A = 45^\circ\) এবং \(B = 15^\circ\) ধরলে,

\[ \tan (45^\circ + 15^\circ) = \frac{\tan 45^\circ + \tan 15^\circ}{1 - \tan 45^\circ \tan 15^\circ} \]

যেহেতু, \(\tan 45^\circ = 1\),

\[ \tan 60^\circ = \frac{1 + \tan 15^\circ}{1 - \tan 15^\circ} \]

সুতরাং,

\[ \frac{1 + \tan 15^\circ}{1 - \tan 15^\circ} = \tan 60^\circ \]

আমরা জানি, \(\tan 60^\circ = \sqrt{3}\). 🎉

অতএব,

\[ \frac{\cos 15^\circ + \sin 15^\circ}{\cos 15^\circ - \sin 15^\circ} = \sqrt{3} \]

উত্তর: \(\sqrt{3}\) ✅