arctan1/2+arctan1/5+arctan1/8=

这种题比较少见啊
你看一下我的方法
因为tan(arctan1/2+arctan1/5)=[tan(arctan1/2)+tan(arctan1/5)]/[1-tan(arctan1/2)*tan(arctan1/5)]=(1/2+1/5)/[1-(1/2)*(1/5)]=7/9
所以arctan1/2+arctan1/5=arctan7/9
又tan(arctan7/9+arctan1/8)=[tan(arctan7/9)+tan(arctan1/8)]/[1-tan(arctan7/9)*tan(arctan1/8)]=(7/9+1/8)/[1-(7/9)*(1/8)]=1
那么arctan7/9+arctan1/8=arctan1=π/4
所以arctan1/2+arctan1/5+arctan1/8
=arctan7/9+arctan1/8
=π/4
如果不懂,请Hi我,祝学习愉快!