题目

sin2x=2sinxcosx怎么推导出来的?
怎么推导的,谢谢COS2X TAN2x也一起吧谢谢

提问时间：2021-03-21

答案

sin(x+x)=sinxcosx+cosxsinx=2sinxcosx
cos(x+x)=cosxcosx-sinxsinx=(cosx)^2-(sinx)^2
另外两个分别加和减1=(sinx)^2+(cosx)^2
sin2x=2sinxcos根据sin(a+b)=sinacosb+cosasinb推出
cos2x=1-(2sinx)^2 or (2cosx)^2-1,同理用
cos(a+b)=cosacosb-sinasinb推导
sin2x
=sin(x+x)
=sinxcosx+cosxsinx
=2sinxcosx
cos2x
=cos(x+x)
=cosxcosx-sinxsinx
=cos^2x-sin^2x
tan2x
=tan(x+x)
=(tanx+tanx)/(1-tanxtanx)
=2tanx/(1-tan^2x)