1. ## proof

Can someone help me on this -

Prove that tan(sin^-1x) = x/sqrt(1-x^2) for |x| < 1 and x not equal to 0

Thanks !

2. Originally Posted by darkangel
Can someone help me on this -

Prove that tan(sin^-1x) = x/sqrt(1-x^2) for |x| < 1 and x not equal to 0

Thanks !
$\tan(\sin^{-1} x) = \frac{\sin (\sin^{-1} x)}{\cos (\sin^{-1} x)} = \frac{x}{\cos (\sin^{-1} x)}$.

$\cos^2 (\sin^{-1} x) = 1 - \sin^2(\sin^{-1} x) = 1-x^2\implies \cos x (\sin^{-1} x) = \sqrt{1-x^2}$ (since the value is positive).

Thus, we get $\frac{x}{\sqrt{1-x^2}}$.

3. Thanks ThePerfectHacker !!