Question

已知角a,b,c,构成公差为pai/3的等差数列,若cosb=-2/3,则cosa+cosb=

Answer 1

∵cosb=-2/3,a=b-π/3,sinb=√5/3

∴cosa=cos(b-π/3)

=cosb*cos(π/3)+sinb*sin(π/3)

=(1/2)cosb+(√3/2)sinb

cosa+cosb=(3/2)cosb+(√3/2)sinb

=(3/2)*(-2/3)+(√3/2)*(√5/3)

=(√15/6)-1