已知cosx+cos(x+π/3)=Acos(x+φ),设A>0,φ∈（-π／2,π／2）则A=____,φ=____.
问题描述：
已知cosx+cos(x+π/3)=Acos(x+φ),设A>0,φ∈（-π／2,π／2）则A=____,φ=____.
答
cosx+cos(x+π/3)
=cos(x+π/6-π/6)+cos(x+π/6+π/6)
=cos(x+π/6)cosπ/6+sin(x+π/6)sinπ/6+cos(x+π/6)cosπ/6-sin(x+π/6)sinπ/6
=2cos(x+π/6)cosπ/6
=（根号3）cos(x+π/6)
所以A=根号3,φ=π/6