Solve for the exact solutions arcsin(x)+arctan(x)=0

Solution:

 

 

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

 

 

The tangent of arcsine is... 
 


so we simplify... 
 
 
 
 
By the zero product rule 
x=0 
or 
 
But the equation can never have a real solution (why?) 

...so x=0