I'm never going to get this...
$\displaystyle \sin(\pi+x) + \cos\left(\frac{\pi}{2} - x\right) + \tan\left(\frac{\pi}{2} + x\right) =$
$\displaystyle \left[\sin(\pi)\cos(x) + \cos(\pi)\sin(x)\right] + \left[\cos\left(\frac{\pi}{2}\right)\cos(x) + \sin\left(\frac{\pi}{2}\right)\sin(x)\right] + \frac{\sin\left(\frac{\pi}{2} + x\right)}{\cos\left(\frac{\pi}{2} + x\right)} =$
finish up by evaluating the first two expansions, then expand the sine and cosine sum in the last fractional term ... finally simplify.