(sin75^o-sin15^o) / (sin75^o +sin15^o) এর মান কত?

Explanation:

Another Explanation (5): bài toán: \(\frac{sin75^\circ - sin15^\circ}{sin75^\circ + sin15^\circ}\) এর মান নির্ণয়। 🤔 আমরা জানি, \(sinC - sinD = 2cos\frac{C+D}{2}sin\frac{C-D}{2}\) এবং \(sinC + sinD = 2sin\frac{C+D}{2}cos\frac{C-D}{2}\) 🤓 অতএব, \(\frac{sin75^\circ - sin15^\circ}{sin75^\circ + sin15^\circ} = \frac{2cos\frac{75^\circ+15^\circ}{2}sin\frac{75^\circ-15^\circ}{2}}{2sin\frac{75^\circ+15^\circ}{2}cos\frac{75^\circ-15^\circ}{2}}\) 😃 \( = \frac{cos\frac{90^\circ}{2}sin\frac{60^\circ}{2}}{sin\frac{90^\circ}{2}cos\frac{60^\circ}{2}}\) 😉 \( = \frac{cos45^\circ sin30^\circ}{sin45^\circ cos30^\circ}\) 😎 \( = \frac{cos45^\circ}{sin45^\circ} \cdot \frac{sin30^\circ}{cos30^\circ}\) 🤩 \( = cot45^\circ \cdot tan30^\circ\) 🥳 আমরা জানি, \(cot45^\circ = 1\) এবং \(tan30^\circ = \frac{1}{\sqrt{3}}\) 🥰 সুতরাং, \(1 \cdot \frac{1}{\sqrt{3}} = \frac{1}{\sqrt{3}}\) ✨ Ans: \(\frac{1}{\sqrt{3}}\) 🎉