Question

The cancellation property sin−1(sin(x)) = x is valid for x in what interval

Answer 1

Answer:

It is given that : $Sin^{-1}(Sin (x) =x$

As we have to find the Domain of $Sin^{-1}(Sin (x)$.

-1 ≤ sin x ≤1

$Sin^{-1}(-1)\leq Sin^{-1}(Sin x)\leq Sin^{-1}(1)\\\frac{-\pi}{2}\leq x\leq \frac{\pi }{2}$

So it is defined for x lying between $(\frac{-\pi}{2}, \frac{\pi }{2})$ .

As meaning of Domain is those values of x for which any function f(x) is defined.