The statement is true because the arcsin function is defined to be the inverse of the sin function.
What are inverse functions?
For invertible function f(x) (this means that f(x) has an inverse) we define the inverse function g(x) such that:
f(g(x)) = x
g(f(x)) = x
Now, particularly for the sin function, arcsin is defined as the inverse function.
Then by definition, arcsin must meet the conditions:
- arcsin(sin(x)) = x
- sin(arcsin(x)) = x
So the answer is true for the definition of the arcsin function.
If you want to learn more about the sin function:
https://brainly.com/question/8120556
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