cos(x+23π)+sin(x+π4)=(cosx⋅cos23π−sinx⋅sin23π)+(sinx⋅cosπ4+cosx⋅sinπ4)\cos\left(x+\frac{2}{3}\pi\right)+\sin\left(x+\frac{\pi}{4}\right)=\left(\cos x\cdot\cos\frac{2}{3}\pi-\sin x\cdot\sin\frac{2}{3}\pi\right)+\left(\sin x\cdot\cos\frac{\pi}{4}+\cos x\cdot\sin\frac{\pi}{4}\right)cos(x+32π)+sin(x+4π)=(cosx⋅cos32π−sinx⋅sin32π)+(sinx⋅cos4π+cosx⋅sin4π) =−12cosx−32sinx+12sinx+12cosx=-\frac{1}{2}\cos x-\frac{\sqrt{3}}{2}\sin x+\frac{1}{\sqrt{2}}\sin x+\frac{1}{\sqrt{2}}\cos x=−21cosx−23sinx+21sinx+21cosx =2−12cosx+2−32sinx=\frac{\sqrt{2}-1}{2}\cos x+\frac{\sqrt{2}-\sqrt{3}}{2}\sin x=22−1cosx+22−3sinx