Question

How do you find the value of `sin (arc sec(x))`?

Answer 1

`sin(arcsec(x))=sqrt(x^2-1)/x`

Explanation:

`arcsecx` means the angle whose secant ratio is `x` i.e. if `arcsec(x)=theta`, we have `sectheta=x`.

As `sectheta=x`, we have `costheta=1/x`

and `sinx=sqrt(1-1/x^2)=sqrt(x^2-1)/x`

Hence, `sin(arcsec(x))=sintheta=sqrt(x^2-1)/x`