sin(arcsin 5/13+arcsin 12/13)=
=sin(arcsin5/13)cos(arcsin12/13)+sin(arcsin12/13)cos(arcsin5/13)=
=5/13*√(1-144/169) + 12/13*√(1-25/169)=5/13*5/13 +12/13*12/13=25/13+144/13=169/13=13
sin(arcsin 5/13+arcsin 12/13)=
=sin(arcsin5/13)cos(arcsin12/13)+sin(arcsin12/13)cos(arcsin5/13)=
=5/13*√(1-144/169) + 12/13*√(1-25/169)=5/13*5/13 +12/13*12/13=25/13+144/13=169/13=13