sinx sin(x+30°) + cosx sin(x+120°) এর মান কত?

Explanation:

Another Explanation (5): ```html sinx sin(x+30°) + cosx sin(x+120°) এর মান নির্ণয়: আমরা জানি, sin(A+B) = sinA cosB + cosA sinB তাহলে, sinx sin(x+30°) + cosx sin(x+120°) = sinx (sinx cos30° + cosx sin30°) + cosx (sinx cos120° + cosx sin120°) = sinx (sinx \(\frac{\sqrt{3}}{2}\) + cosx \(\frac{1}{2}\)) + cosx (sinx (-\(\frac{1}{2}\)) + cosx \(\frac{\sqrt{3}}{2}\)) = \(\frac{\sqrt{3}}{2}\) sin²x + \(\frac{1}{2}\) sinx cosx - \(\frac{1}{2}\) sinx cosx + \(\frac{\sqrt{3}}{2}\) cos²x = \(\frac{\sqrt{3}}{2}\) sin²x + \(\frac{\sqrt{3}}{2}\) cos²x = \(\frac{\sqrt{3}}{2}\) (sin²x + cos²x) আমরা জানি, sin²x + cos²x = 1 অতএব, \(\frac{\sqrt{3}}{2}\) (1) = \(\frac{\sqrt{3}}{2}\) ✨ সুতরাং, sinx sin(x+30°) + cosx sin(x+120°) = \(\frac{\sqrt{3}}{2}\) 🎉 ```