sin^2 (π/8) + sin^2 (5π/8) এর মান কত?

Explanation:

Another Explanation (5): প্রশ্ন: \( \sin^2 \left(\frac{\pi}{8}\right) + \sin^2 \left(\frac{5\pi}{8}\right) \) এর মান নির্ণয় করো। 🧐 আমরা জানি, \( \sin(\theta) = \cos\left(\frac{\pi}{2} - \theta\right) \) তাহলে, \( \sin\left(\frac{5\pi}{8}\right) = \sin\left(\pi - \frac{3\pi}{8}\right) = \sin\left(\frac{3\pi}{8}\right) \) 🥳 আবার, \( \sin\left(\frac{3\pi}{8}\right) = \sin\left(\frac{\pi}{2} - \frac{\pi}{8}\right) = \cos\left(\frac{\pi}{8}\right) \) 🤩 সুতরাং, \( \sin^2 \left(\frac{5\pi}{8}\right) = \cos^2 \left(\frac{\pi}{8}\right) \) 🤓 এখন, \( \sin^2 \left(\frac{\pi}{8}\right) + \sin^2 \left(\frac{5\pi}{8}\right) = \sin^2 \left(\frac{\pi}{8}\right) + \cos^2 \left(\frac{\pi}{8}\right) \) 😎 আমরা জানি, \( \sin^2(\theta) + \cos^2(\theta) = 1 \) 🥰 অতএব, \( \sin^2 \left(\frac{\pi}{8}\right) + \sin^2 \left(\frac{5\pi}{8}\right) = 1 \) 🎉