Write tan sin1 x x 1 as an algebraic expression in terms of

Write tan (sin^-1 x), |x| < 1, as an algebraic expression in terms of x. Explain your answer.

Solution

tan(sin^-1(x) ) , |x| <1

Let y = sin^-1(x)

siny = x

tany = x/sqrt(1- x^2)

y = tan^-1[x/sqrt(1- x^2)]

So, tan(sin^-1(x) ) = tantan^-1[x/sqrt(1- x^2)]

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