设α、β、γ∈R,且sinα+sinγ=sinβ,cosα+cosγ=cosβ,则α-β()

题目

设α、β、γ∈R,且sinα+sinγ=sinβ,cosα+cosγ=cosβ,则α-β()
-π/3 π/6 -π/3或π/3 π/3

答案

sinγ=sinβ - sinα,cosγ=cosβ - cosα(sinβ - sinα)^2 +(cosβ - cosα)^2 = (sinγ)^2 + (cosγ)^2 = 1 (1)同时展开 (sinβ - sinα)^2 +(cosβ - cosα)^2 =2 - 2 (sinβ sinα + cosβ cosα）= 2 - 2cos(...