how we cancel sin by arcsin?

and also arcsin is not the reciprocal of sin...

You cannot cancel sin-1x and sinx , as both are not reciprocal of each other .
If you have sin-1(sinx) , then it is equal to x . Vice versa is also true.
Here suppose x = 45 , then sin45 = 1/(2)1/2 , and sin-1(1/(2)1/2 ) = pi/4
So here first find sinx and then find its  inverse .

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@Tannu

we dont cut off sin with arcsin or the viceversa. The thing which takes place there is lyk given with an example:-

sin(sin-1(1)) = sin (pi/2)................... [since sin-1(1) is pi/2]

=1

exactly the thing that we do here is we find inverse of sin after finding sin so it easy to explain in terms of cancelling out.

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