sin(A-30°)+sin(A+150°)=? 

প্রশ্ন: sin(A-30°) + sin(A+150°) = ?

আমরা জানি, sin(C) + sin(D) = 2 sin((C+D)/2) cos((C-D)/2)

এখানে, C = A - 30° এবং D = A + 150°

অতএব, \( \begin{aligned} sin(A-30°) + sin(A+150°) &= 2 sin(\frac{(A-30°) + (A+150°)}{2}) cos(\frac{(A-30°) - (A+150°)}{2}) \\ &= 2 sin(\frac{2A + 120°}{2}) cos(\frac{-180°}{2}) \\ &= 2 sin(A + 60°) cos(-90°) \end{aligned} \)

আমরা জানি, cos(-θ) = cos(θ) এবং cos(90°) = 0

সুতরাং, \( \begin{aligned} 2 sin(A + 60°) cos(-90°) &= 2 sin(A + 60°) \cdot 0 \\ &= 0 \end{aligned} \)

সুতরাং, sin(A-30°) + sin(A+150°) = 0

উত্তর: 0 🎉