Answer:
[tex]sin(cos^{-1}x)=\sqrt{1-x^2}[/tex]
Step-by-step explanation:
let us assume
[tex]cos^{-1} x=\theta\\x=cos\theta\\[/tex]
now
[tex]sin(cos^{-1}x)[/tex] can be written as [tex]sin\theta[/tex]
we know [tex]sin^2\theta+cos^2\theta=1[/tex]
so [tex]sin^2\theta=1-cos^2\theta[/tex]
[tex]sin\theta=\sqrt{1-cos^2\theta}[/tex]
now from above equation we can say that
[tex]sin\theta=\sqrt{1-x^2}[/tex]
[tex]sin(cos^{-1}x)=\sqrt{1-x^2}[/tex]
