Write the composed trigonometric function sin(arctan x) in terms of x. Explain your steps and/or show your work. Remember to rationalize the denominator if necessary.

Answer 1

I will just do one, then you try
draw right triangle A B C, C is right angle. angle at A is arc tan x
let side AC =1
side BC = x
side AC = sqrt(x^2 + 1)
sin A = x/sqrt(x^2+1)
= x sqrt(x^2+1) / ( x^2+1)

Answer 2

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Answer 3

same