Acute Angles and a Parameter

Problem

Suppose there exist $\alpha, \beta$ with $\alpha$ , $\beta$ , and $\alpha + \beta$ all acute, satisfying

\sin\frac{\alpha}{2} = k\cos\beta.

Find the range of possible values of $k$ .

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Extrema, Monotonicity

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