tan x=-2
sinx=-2cosx
sin²x＋cos²x=1
5cos²x=1
cosx=-√5/5
sinx=2√5/5
所以
sin(x+π/6)
=sinxcosπ/6+cosxsinπ/6
=2√5/5×√3/2-√5/5×1/2
=(2√15-√5)/10