Question 1003933
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Let {{{alpha}}} = arctan(x).


Then {{{tan(alpha)}}} = x = {{{sin(alpha)/cos(alpha)}}}             -----> 


{{{x^2}}} = {{{sin^2(alpha)/cos^2(alpha)}}} = {{{sin^2(alpha)/(1 - sin^2(alpha))}}}     -----> 


{{{x^2*(1 - sin^2(alpha))}}} = {{{sin^2(alpha)}}}         ----->


{{{x^2}}} - {{{x^2}}}.{{{sin^2(alpha)}}} = {{{sin^2(alpha)}}}       ----->


{{{x^2}}} = {{{(1+x^2)}}}.{{{sin^2(alpha)}}}                 -----> 


{{{sin^2(alpha)}}} = {{{(x^2)/(1 + x^2)}}},


{{{sin(alpha)}}} = {{{sqrt((x^2)/(1+x^2))}}} = +/- {{{(abs(x))/(sqrt(1+x^2))}}} = {{{x/(sqrt(1+x^2))}}}.


Finally,   sin(arctan(x)) = {{{x/(sqrt(1+x^2))}}}.


Is this what you want?