Simplify the following expression into an algebraic one that

Simplify the following expression into an algebraic one, that is, without any trig or inverse trig functions:

tan(arcsin(x))

Solution

tan (arc sin (x ))

let arc sin x = y

sin y = x

perpoendicular / hypotenuse = x/1

base = sqrt ( 1 - x^2 )

tan (y ) = perpendicular / base

= x / sqrt (1-x^2 )

or

tan ( arc sin (x)) =x / sqrt (1 - x^2 )