4. Solve the system $\left\{\begin{array}{c}x^{2}+y^{2}=1 \\ \arccos x-\arcsin y=a\end{array}\right.$ for any $a$.
Answer: 1) $\left\{\begin{array}{l}x_{1}=\cos \varphi \\ y_{1}=\sin \varphi\end{array}, \varphi \in\left[0 ; \frac{\pi}{2}\right]\right.$ when $\left.a=0 ; 2\right)\left\{\begin{array}{l}x_{1}=-\sin \frac{a}{2} \\ y_{1}=\cos \frac{a}{2}\end{array},\left\{\begin{array}{l}x_{2}=\cos \frac{a}{2} \\ y_{2}=-\sin \frac{a}{2}\end{array}\right.\right.$ when $\varphi \in(0 ; \pi)$;

3) $\left\{\begin{array}{l}x_{1}=\cos \varphi \\ y_{1}=\sin \varphi\end{array}, \varphi \in\left[\pi ; \frac{3 \pi}{2}\right]\right.$ when $a=\pi ;$ 4) $\varnothing$ when $a \notin[0 ; \pi]$.