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, $sin(sin^-1(x))= x$