c: \(C=\sin\left(\frac32\pi+x\right)+\sin\left(5\pi+x\right)+cos\left(\frac52\pi-x\right)+cos\left(\frac{\pi}{2}+x\right)\)
\(=\sin\left(x-\frac{\pi}{2}+2\pi\right)+\sin\left(4\pi+\pi+x\right)+cos\left(2\pi+\frac{\pi}{2}-x\right)+cos\left(\frac{\pi}{2}+x\right)\)
\(=\sin\left(x-\frac{\pi}{2}\right)+\sin\left(\pi+x\right)+cos\left(\frac{\pi}{2}-x\right)+cos\left(\frac{\pi}{2}+x\right)\)
\(=\left(\sin x\cdot cos\left(\frac{\pi}{2}\right)-cosx\cdot\sin\left(\frac{\pi}{2}\right)\right)+\left(\sin\pi\cdot cosx+\sin x\cdot cos\pi\right)+\sin x+\left(cos\left(\frac{\pi}{2}\right)\cdot cosx-\sin\left(\frac{\pi}{2}\right)\cdot\sin x\right)\)
\(=-cosx-\sin x+\sin x+\left(-\sin x\right)=-\sin x-cosx\)
