已知角α,β,γ构成公差为π/3的等差数列,若cosβ=-2/3,则cosα+cosγ=
问题描述：
已知角α,β,γ构成公差为π/3的等差数列,若cosβ=-2/3,则cosα+cosγ=
答
α=β-π/3,γ=β+π/3
cosα+cosγ
=cos(β-π/3)+cos(β+π/3)
=cosβcosπ/3+sinβsinπ/3+cosβcosπ/3-sinβsinπ/3
=2cosβcosπ/3
=2X(-2/3)X(1/2)
=-2/3