Simplify the expression. sin(tan−1(x))

Question

Simplify the expression.
sin(tan−1(x))

Answer 1

consider a right triangle in which acute angle θ has tan θ = x, i.e. θ = tan^-1x.  I suggest that you draw it.

This means that the other leg has to be 1 and by Pythagoras, hypotenuse = √(1+x²).

 

sin θ = sin(tan^-1x) = x/√(1+x²).