Find the maximum value of
\[\sin \frac{\theta}{2} \cdot (1 + \cos \theta)\]for $0 < \theta < \pi.$
Question:
Find the maximum value of
\[\sin \frac{\theta}{2} \cdot (1 + \cos \theta)\]for $0 < \theta < \pi.$
Answer:
Let's think step by step.

user
\frac{4 \sqrt{3}}{9}
Find the maximum value of
\[\sin \frac{\theta}{2} \cdot (1 + \cos \theta)\]for $0 < \theta < \pi.$
train