sinx+sin(120°+x)=?

Explanation:

Another Explanation (5): sin(x) + sin(120° + x) = ? আমরা জানি, sin(A + B) = sin(A)cos(B) + cos(A)sin(B) তাহলে, sin(120° + x) = sin(120°)cos(x) + cos(120°)sin(x) = \( \frac{\sqrt{3}}{2} \)cos(x) - \( \frac{1}{2} \)sin(x) 🤯 অতএব, sin(x) + sin(120° + x) = sin(x) + \( \frac{\sqrt{3}}{2} \)cos(x) - \( \frac{1}{2} \)sin(x) = \( \frac{1}{2} \)sin(x) + \( \frac{\sqrt{3}}{2} \)cos(x) ✨ এখন, আমরা যদি \( \frac{1}{2} \) এবং \( \frac{\sqrt{3}}{2} \) কে cos(60°) এবং sin(60°) দিয়ে প্রতিস্থাপন করি, তাহলে পাই: = cos(60°)sin(x) + sin(60°)cos(x) 🤩 আমরা জানি, sin(A + B) = sin(A)cos(B) + cos(A)sin(B) সুতরাং, cos(60°)sin(x) + sin(60°)cos(x) = sin(x + 60°) 🥳 অতএব, sin(x) + sin(120° + x) = sin(x + 60°) ✅