Rewrite the expression as an algebraic expression of x Rewri

Rewrite the expression as an algebraic expression of x:

Rewrite the expression as an algebraic expression of x: sin (tan^-1 x)

Solution

sin(tan^-1x)

let tan^-1x=t

Therefore tan t= x

Here opposite=x and adjacent=1

Therefore hypotenuse=sqrt(1²+x²) = sqrt(1+x²)

sin t=opposite/hypotenuse= x/sqrt(1+x²) x(sqrt(1+x²))/(1+x²)

Hence,sin(tan^-1x)= x(sqrt(1+x²))/(1+x²)