Find a formula relating $\operatorname{arcsin}(x)$ and $\operatorname{arccos}⁡(x)$ 
From the formula $\sin\left(\frac{π}{2}−x\right)=\cos x$, find a formula relating $\operatorname{arcsin}(x)$ and $\operatorname{arccos}⁡(x)$.

I have figured out that the domain of $x$ is $[-1;1]$, but I have no idea how to do this. I've tried letting $y=\cos x$ and the only result I've got is $$\operatorname{arccos}(y)+\operatorname{arcsin}(y)=\frac{π}{2}$$
I need a full answer.

Your question is like:
In a right angled triangle cos of one acute angle  $ \alpha = x/\sqrt{x^2+y^2}  $ and sine  of the other  acute angle  $ \beta  = y/\sqrt{x^2+y^2}. $ Find relation between $ \alpha,\beta. $
Answer is provided by the direct definition of the trig ratios as : $ \alpha+ \beta = \pi/2. $
