\(=cos\left(4\pi+\pi+a\right)-sin\left(6\pi-\dfrac{\pi}{2}-a\right)-\dfrac{1}{2}+\dfrac{1}{2}cos\left(\dfrac{\pi}{2}+a\right)-\dfrac{1}{2}sina\)
\(=cos\left(\pi+a\right)-sin\left(-\dfrac{\pi}{2}-a\right)-\dfrac{1}{2}-\dfrac{1}{2}sina-\dfrac{1}{2}sina\)
\(=-cosa+cosa-\dfrac{1}{2}-sina\)
\(=-\dfrac{1}{2}-sina\)