π－arctan(3/2)－arctan(2/3)=?
问题描述：
π－arctan(3/2)－arctan(2/3)=?
答
设arctan(3/2)=A,arctan(2/3)=B
所以tanA=3/2>0,tanB=2/3>0
又因为A,B属于[-π/2,π/2]
所以A,B都为锐角
tanA*tanB=1,故A和B互余
A+B=π/2
π－arctan(3/2)－arctan(2/3)=π/2