Question

cos(3arctg(-1/3))
sin(2arctg(-1))

Answer 1

1) cos(3arctg(-1/√3))=cos(-3arctg 1/√3)=cos(3arctg 1/√3)=cos(3*π/6)=cos π/2=0.
2) sin(2arctg(-1))=sin(-2arctg 1)=-sin(2arctg 1)=-sin(2*π/4)=-sin π/2=-1.