Question

How do you calculate `sin(arcsin 2x)`?

Answer 1

It will be `2x`

`arcsin 2x` means find the angle of which the sine is `2x`

`sin` means find the sine.
So you first find the angle, and take the sine of it.

So the real question is:
Find the sine of the angle that 'belongs' to a sine of `2x`

In short
`sin` and `arcsin` are two opposing operations, they cancel each other out, just like square and square root.

There are limitations, since `sin` must be between `-1` and `+1`,
so `2x` is also limited to these boundaries:

`-1/2<=x<=+1/2`