What is the maximum value of $f(\theta) = \sin\theta \cos\theta$ What is the maximum value of $f(\theta) = \sin\theta \cos\theta$ ?

Hint $1$:
$\sin \theta \cdot \cos \theta = \dfrac{\sin 2\theta}{2}$
Hint $2$:
$\sin \theta \cdot \cos \theta \leq \dfrac{\sin^2 \theta + \cos^2 \theta}{2} = \dfrac{1}{2}$.
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