(4sin55°+cos145°)^2+(4cos55°+145°)^2
(4sin55°+cos145°)²+(4cos55°-sin145°)²=
=(4sin55°+cos(90°+55°))²+(4cos55°-sin(90°+55°))²=
=(4sin55°-sin55°)²+(4cos55°-cos55°)²=
=(3sin55°)²+(3cos55°)²=
=9sin²55°+9cos²55°=
=9(sin²55°+cos²55°)=
=9•1=9 (Ответ)