To completely show how this can be simplified to -2sin(x), use angle sum formulas for sin/cos.
[tex]cos (a+b) = cos (a) cos (b) - sin (a) sin (b) \\ sin(a+b) = sin (a) cos (b) + sin (b) cos (a)[/tex]
Apply to given problem:
[tex]=cos (x) cos (\frac{\pi}{2}) - sin (x) sin (\frac{\pi}{2}) +sin (x) cos (\pi) + sin (\pi) cos (x) \\= 0-sin(x) -sin(x)+0 \\ = -2 sin (x)[/tex]
