Question 743897
{{{arcsin(x)+arctan(x)=0}}}


{{{arctan(x)=-arcsin(x)}}}


arcsine is an odd function so we "pull" the negative sign into the input...


{{{arctan(x)=arcsin(-x)}}}


{{{tan(arctan(x))=tan(arcsin(-x))}}}


The tangent of arcsine is...

{{{x/sqrt(1-x^2)}}}



so we simplify...

{{{x=(-x)/sqrt(1-x^2)}}}

{{{x*sqrt(1-x^2)=-x}}}

{{{x*sqrt(1-x^2)+x=0}}}

{{{x*(sqrt(1-x^2)+1)=0}}}

By the zero product rule

x=0

or 

{{{sqrt(1-x^2)+1=0}}}

But the equation can never have a real solution (why?)


...so x=0