Question

How do you simplify the expression `sin(arctan x)`?

Answer 1

`sin(arctan x)=x/(+-sqrt(x^2+1))`

Explanation:

The solution:

`arctan x` is an angle whose tangent function `=x/1`

Considering the sides of the right triangle. We have opposite side `=x`, adjacent side `=1` and hypotenuse `=sqrt(x^2+1)`

Therefore the sine of this angle `=("opposite side")/("hypotenuse")=x/sqrt(x^2+1)`

God bless....I hope the explanation is useful.