已知cos（a+π/3）＝1/4,则cos a等于多少?为什么?

题目

已知cos（a+π/3）＝1/4,则cos a等于多少?为什么?

答案

cos(a+π/3)=1/4
sin(a+π/3)=±√[1-cos²(a+π/3)]=±√15/4
cosa=cos[(a+π/3)-(π/3)]
=cos(a+π/3)cos(π/3)+sin(a+π/3)sin(π/3)]
=(1/4)*(1/2)+(±√15/4)*(√3/2)
=(1±3√5)/8