Product Of Sine And Cosine

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 $a+b$ .