Question

Rewrite the expression as an algebraic expression in x. tan(sin−1(x))

Answer 1

Let $tan^{-1} x=\alpha$
Then it can be shown by using a right-angled triangle and the rule of Pythagoras that $\alpha= tan^{-1} \frac{x}{ \sqrt{1-x^{2}} }$
Therefore
$tan(sin ^{-1} (x))=\frac{x}{ \sqrt{1-x^{2}} }$