1.证明tanx+tany=tan(x+y)-tanxtanytan(x+y)2.求tan20度+tan40度+根下3倍tan20度tan40度

问题描述:

1.证明tanx+tany=tan(x+y)-tanxtanytan(x+y)
2.求tan20度+tan40度+根下3倍tan20度tan40度

1.
tan(x+y)=tanx+tany/1-tanxtany 所以
tanxtany=tan(x+y)*(1-tanxtany) 展开得
tanx+tany=tan(x+y)-tanxtanytan(x+y)

tan(x+y)=(tanx+tany)/(1-tanxtany)
整理得tanx+tany=tan(x+y)-tanxtanytan(x+y)
tan20+tan40+√3tan20tan40
=tan60-tan60tan20tan40+√3tan20tan40
=tan60=√3