Question

Is sin(sin^-1(x)) = sin^-1(sinx) an identity?

Answer 1

yes...they are both equal to x

Answer 2

I don't understand what you mean? I don't really understand this much, is there a way that you can explain it to me in details a little bit more.

Answer 3

Hey, when you take the arcsin (sin^-1) of a sin function, it's basically like saying (1/3) x (3) = 1, or (2/7) x (7/2) = 1 (this is the best example i could come up with to show you that it cancels out).
Same thing with other functions, arctan of tan will cancel out and leave you with the original function, etc . This is what the person above me means, the arcsin and sin canceled out and left you the x.
By the way, the equation above is the same on each side. That's like saying:
2x + 7 = 7 + 2x