Question

Sin(arcsin^-1(x))=x for -1<x<1 TRUE OR FALSE?

Answer 1

answer : true

`sin(sin^-1(x))= x`

Proof:

Lets assume
`(sin^-1(x))= y`

When we move sin^-1 to the other side it becomes sin

so x= sin(y)

Now we replace it on the left hand side

`sin(sin^-1(x))`

`sin(y)` = x (Right hand side)

Hence proved,
`sin(sin^-1(x))= x`