Cos1°+cos2°+cos3°+……cos89°=

原式中不是求平方和哈，那么第二种做法好像有问题哟！

乘以sin0.5
0.5*(sin1.5-sin0.5)+0.5*sin(sin2.5-sin1.5)+...+0.5*(sin89.5-sin88.5)=0.5*(sin89.5-sin0.5)
原式=0.5*cot0.5-0.5

由Sin（A+B）=SinACosB+CosASinB
Sin（A-B）=SinACosB-CosASinB
则Sin（A+B）+Sin（A-B）=2SinACosB
Cos1°+cos2°+cos3°+……cos89°
=2Sin1°（Cos1°+cos2°+cos3°+……cos89°）/2Sin1°
=(2 Sin1°Cos1°+2 Sin1°Cos2°+2 Sin1°Cos3°+•••+2 Sin1°Cos88°+2 Sin1°Cos89°)/ 2Sin1°
=(Sin2°+ Sin0°+ Sin3°+ Sin(-1)°+ Sin4°+ Sin(-2)°+•••+ Sin89°+ Sin(-87)°+ Sin90°+ Sin(-88)°)/ 2Sin1°
=(Sin2°+ Sin0°+ Sin3°- Sin1°+ Sin4°- Sin2°+•••+ Sin89°- Sin87°+ Sin90°- Sin88°)/ 2Sin1°
=( Sin90°- Sin1°)/ 2Sin1°
=(1- Sin1°)/ 2Sin1°