已知cosa=1/3,cos(a+b)=-1/3,且a,b属于(0,派/2),则cos(a-b)的值等于
问题描述:
已知cosa=1/3,cos(a+b)=-1/3,且a,b属于(0,派/2),则cos(a-b)的值等于
答
cosb/3-根8sinb/3=-1/3cosb-根8sinb=-1(cosb+1)^2=8sin^2bcos^2b+2cosb+1=8-8cos^2b9cos^2b+2cosb-7=0(9cosb-7)(cosb+1)=0cosb=7/9cos(a+b)+cos(a-b)=2cosacosb-1/3+cos(a-b)=14/27cos(a-b)=23/27