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).

1. 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)