Question

Re write tan(sin^-1(x)) as an algebraic expression

Answer 1

Sketch a right triangle with base 1 and vertical leg = x. That is that angle whose tan is x. 

Now compute the hypotenuse = √(x² + 1). 

Read off the sine of the base angle (which is tan ˉ¹x) as x/√(x² + 1) 

Done