Hard trigonometry ..plz help?

Question

RATIONALIZE THE DENOMINATOR

tan [sin^-1 (x)] = x / √(1 - x²).

Answer 1

Draw a right triangle with hypotenuse = 1 and one side = x.
Then the 3rd side must be sqrt(1-x^2).
Let z be the angle between the hypotenuse and the side = sqrt(1-x^2).
Then z = sin^-1 x/1 = sin^-1 x
So tan (sin^-1 x) = tan z = x/sqrt(1-x^2)
= [xsqrt(1-x^2)]/(1-x^2)