已知0≤x≤π/3,5√3*sinx+5cosx=8 求 tan(x+π/6).
问题描述：
已知0≤x≤π/3,5√3*sinx+5cosx=8 求 tan(x+π/6).
答
5√3*sinx+5cosx=8
10(sinxcosπ/6+cosxsinπ/6)=8
10sin(x+π/6)=8
sin(x+π/6)=0.8
0≤x≤π/3
π/6≤x+π/6≤π/2
cos(x+π/6)=√(1-0.8²)=0.6
tan(x+π/6)=0.8/0.6=4/3