$\color{Orange}{\text{~Orange~}}$

Ta có

`\sin(\alpha)=\cos(90^@-\alpha)`

Do đó

`A=(\sin(1)+\sin(2)+\sin(3)+...+\sin(88)+\sin(89))-(\cos(1)+\cos(2)+\cos(3)+...+\cos(88)+\cos(89))`

`=(\cos(90-1)+\cos(90-2)+\cos(90-3)+...+\cos(90-88)+\cos(90-89))-(\cos(1)+\cos(2)+\cos(3)+...+\cos(88)+\cos(89))`

`=(\cos(89)+\cos(88)+\cos(87)+...+\cos(2)+\cos(1))-(\cos(1)+\cos(2)+\cos(3)+...+\cos(88)+\cos(89))`

`=0`