# SineCosine at its pinnacle

Geometry Level 3

Let the maximum value of $$(\sin x \cos x)$$ for $$x \in \mathbb{R}$$ be $$M$$ . If the value of $$x$$ for which $$(\sin x \cos x)$$ is maximum satisfying $$0< x < \pi$$ can be expressed as $$\dfrac{A\pi}{B}$$ for co-prime integers $$A,B$$ , compute $$M+A+B$$.

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