Question

simplify: f(x,y)= arcsin(sin(x+y))

Answer 1

     Just use the definition of arcsin that is given by:

$\left \{ {{sen \alpha =x} \atop {arcsinx= \alpha }} \right. \\ \\ arcsin(sen \alpha )= \alpha$
 
     Therefore:

$f(x,y)=arcsin(sen(x+y)) \\ \boxed {f(x,y)=x+y}$

If you notice any mistake in my english, please let me know, because i am not native.