# Product Of Sine And Cosine

Geometry Level 2

Determine the values of $$k$$ so that the inequality $$\displaystyle{\sin x \cos x\geq k}$$ is satisfied $$\forall x \in \mathbb{R}$$.

If $$k^2$$ can be written as $$\displaystyle \frac{a}{b}$$, where $$a$$ and $$b$$ are relatively prime integers, find $$a+b$$.

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