Step 1 :\cos\left(x+\frac{\pi}{2}\right)=-\sin(x), \sin\left(x+\frac{\pi}{2}\right)=\cos(x), \cos\left(x-\frac{\pi}{2}\right)=\sin(x), -\sin\left(x-\frac{\pi}{2}\right)=-\cos(x)
Step 2 :A(x)=-\sin(x)+\cos(x)+\sin(x)-\cos(x)=2\cos(x)
Step 3 :2\cos(x)=\sqrt{2} \Rightarrow \cos(x)=\frac{\sqrt{2}}{2} \Rightarrow x=\frac{\pi}{4}+2k\pi \text{ or } x=-\frac{\pi}{4}+2k\pi \Rightarrow x=\frac{\pi}{4}+k\pi
Step 4 :2\cos(x)<\sqrt{2} \Rightarrow -1<\cos(x)<\frac{\sqrt{2}}{2} \Rightarrow x\in ]-\pi, \frac{-3\pi}{4}] \cup ]\frac{-\pi}{4}, \frac{\pi}{4}] \cup [\frac{3\pi}{4}, \pi]