已知α=-π/3,β=2π/3,求sinα+cosβ/tanα×tanβ的值.
问题描述：
已知α=-π/3,β=2π/3,求sinα+cosβ/tanα×tanβ的值.
答
sinα+cosβ/tanα×tanβ=sin(-π/3)+cos(2π/3)/tan(-π/3)×tan(2π/3)
=-sin(π/3)-cos(π/3)/(-tanπ/3)×(-tanπ/3)
=-√3/2-(1/2)/3
=-(3√3+1)/6