Necessary First, Sufficient Second

Problem

Suppose $a, b \in \mathbb{R}$ satisfy

3a(\sin x + \cos x) + 2b\sin 2x \le 3 \qquad\text{for all } x \in \mathbb{R}.

When $a + b$ attains its minimum value, what is $a$ ?

Answer

Solution

Difficulty	7/10
Topics	functions, trigonometry

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