若sinα是方程6x=1-√x的根,试求tan(π-α)tan(2π-α)cos(5π-α)/cos(3π/2+α)的值

化简：tan(π-α)tan(2π-α)cos(5π-α)/cos(3π/2+α) = -tanα
解根号方程：6x+√x-1=0
x=1/3（舍去负根）
所以：sinα = 1/3
因α没有限制,所以α可能锐角可能钝角
若α锐角
tanα = √2/4
tan(π-α)tan(2π-α)cos(5π-α)/cos(3π/2+α) = -√2/4
若α钝角
tanα = -√2/4
tan(π-α)tan(2π-α)cos(5π-α)/cos(3π/2+α) = √2/4