Só para confirmar!
[tex]\begin{cases} \sin (x + y) = \sin x \cdot \cos y + \sin y \cdot \cos x \\ \sin (x - y) = \sin x \cdot \cos y - \sin y \cdot \cos x\end{cases}[/tex]
[tex]E = \sin (- x) + \sin (\pi + x) - \sin \left ( \frac{\pi }{2} - x \right )[/tex]
[tex]E = \sin (0 - x) + \sin (\pi + x) - \sin \left ( \frac{\pi }{2} - x \right )[/tex]
[tex]E = (\sin 0 \cdot \cos x - \sin x \cdot \cos 0) + (\sin \pi \cdot \cos x + \sin x \cdot \cos \pi) - \left [ \sin \left ( \frac{\pi}{2} \right ) \cdot \cos x - \sin x \cdot \cos \left ( \frac{\pi }{2} \right ) \right ][/tex]
[tex]E = 0 \cdot \cos x - \sin x \cdot 1 + 0 \cdot \cos x + \sin x \cdot - 1 - (1 \cdot \cos x - \sin x \cdot 0)[/tex]
[tex]E = 0 - \sin x + 0 - \sin x - \cos x + 0[/tex]
[tex]\boxed{E = - 2 \cdot \sin x - \cos x}[/tex]
