cos15° এর মান-

cos15° এর মান নির্ণয়:

আমরা জানি, cos(A - B) = cosA cosB + sinA sinB

cos15° = cos(45° - 30°) 🤩

সুতরাং, cos15° = cos45° cos30° + sin45° sin30° 🥰

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

অতএব, cos15° = \( \frac{1}{\sqrt{2}} \cdot \frac{\sqrt{3}}{2} + \frac{1}{\sqrt{2}} \cdot \frac{1}{2} \)

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

= \( \frac{\sqrt{3} + 1}{2\sqrt{2}} \) 😍

এখন, লব ও হরকে \( \sqrt{2} \) দিয়ে গুণ করে পাই,

cos15° = \( \frac{(\sqrt{3} + 1)\sqrt{2}}{2\sqrt{2} \cdot \sqrt{2}} \)

= \( \frac{\sqrt{6} + \sqrt{2}}{4} \) 🤯

অথবা, cos15° = \( \frac{\sqrt{2}(\sqrt{3} + 1)}{4} \) 😇

বিকল্প পদ্ধতি:

cos15° = √(1 + cos30°)/2

= √(1 + √3/2)/2

= √(2 + √3)/4

= 1/2 √(2 + √3)

সুতরাং, cos15° = \( \frac{\sqrt{6} + \sqrt{2}}{4} \) অথবা cos15° = 1/2√(2+√3) । 🎉