Rewrite the expression as an algebraic expression in x tan s

Rewrite the expression as an algebraic expression in x. tan (sin^-1 x) a. 1/Squareroot x^2 - 1 b. Squareroot x^2 - 1 c. Squareroot 1 - x^2 d. x/Squareroot 1 - x^2

Solution

tan(sin^-1x)

sin^-1x=t

x=sin t

opposite=x

hypotenuse=1

adjacent=sqrt(1-x²)

tan t=x/sqrt(1-x²)

tan(sin^-1x)=x/sqrt(1-x²)

correct option is d.