Question

已知cos(75°-α)=-1/3,且-180°<α<-120°,求cos(105°+α)+cos(15°+α)的值

Answer 1

已知-180°<α<-120°，那么：120°<-α<180°
有：195°<75°-α<255°
即角75°-α是第三象限角
已知cos(75°-α)=-1/3，所以：sin(75°-α)=-根号[1-cos²(75°-α)]=-(2根号2)/3
又cos(75°-α)=cos[180°-(105°+α)]=-cos(105°+α)
那么：cos(105°+α)=-cos(75°-α)=1/3
而sin(75°-α)=sin[90°-(15°+α)]=cos(15°+α)=-(2根号2)/3
所以：cos(105°+α)+cos(15°+α)=1/3 - (2根号2)/3=(1- 2根号2)/3