【急】推导诱导公式 cos(π/2+α)=-sinα tan(π/2+α)=-cotα cot(π/2+α)=-tan

问题描述:

【急】推导诱导公式 cos(π/2+α)=-sinα tan(π/2+α)=-cotα cot(π/2+α)=-tan

cos(π/2+α)=sin[π/2-(π/2+α)]=sin(-α)=-sinα
sin(π/2+α)=cos[π/2-(π/2+α)]=cos(-α)=cosα
tan(π/2+α)=sin(π/2+α)/cos(π/2+α)=cosα/-sinα=-cotα
cot(π/2+α)=cos(π/2+α)/sin(π/2+α)=-sinα/cosα=-tanα

cos(π/2+α)=cosπ/2cosα-sinπ/2sinα=-sinα
tan(π/2+α)=sin(π/2+α)/cos(π/2+α)=cosα/(-sinα)=-cotα
cot(π/2+α)=cos(π/2+α)/sin(π/2+α)=-sinα/cosα=-tanα

cos(π/2+α)=-sinα ,tan(π/2+α)=-cotα,cot(π/2+α)=-tan诱导公式.推导过程如下:sin(π/2+α)= cos αsin(π+α) =sin[π/2+(π/2+α)]= cos(π/2+α)又sin(π+α) = - cosα) 所以:cos(...