[tex]E = sin\Big(\dfrac{x}{2} \Big) \cdot cos\Big(\dfrac{x}{2} \Big) = \dfrac{2\cdot sin\Big(\dfrac{x}{2} \Big) \cdot cos\Big(\dfrac{x}{2} \Big) }{2} = \dfrac{sin\Big( 2 \cdot \dfrac{x}{2} \Big)}{2} = \dfrac{sinx}{2} \\ \\ \\ -1\leq sinx\leq 1 \Big|\cdot \Big(\dfrac{1}{2} \Big) \Rightarrow -\dfrac{1}{2}\leq \dfrac{sinx}{2}\leq \dfrac{1}{2} \\ \\ \Rightarrow $Valoarea maxima a lui E este $ \dfrac{1}{2} [/tex]
