题目

已知cos(α+5π/12)=1/3,且-π

提问时间：2020-07-27

答案

-π<α<-π/2,
-π+5π/12<α+5π/12<-π/2+5π/12
-7π/12<α+5π/12<-π/12
cos(α+5π/12)=1/3
-π/2<α+5π/12<-π/12
cos(π/12-α)
=cos[(π/2-5π/12)-α]
=cos[π/2-(5π/12+α)]
=sin(5π/12+α)
=-2√2/3
cos(7π/12-α)
=cos[(π-5π/12)-α]
=cos[π-(5π/12+α)]
=-cos(α+5π/12)
=-1/3
cos(α+17π/12)
=cos(π+α+5π/12)
=-cos(α+5π/12)
=-1/3