已知函数f(x)=x+2xsina-1,x属于[-√3/2.1/2] (1)求a=π/6时,求f(x)的最大值和最小值

(1)a=π/6,则f(x)=x+√3x-1=(x+√3/2)-7/4 ∴f(x)在(-∞,-√3/2)单调减,(√3/2,+∞)单调增 又x∈[-√3/2,1/2] ∴f(x)在定义域单调增 当x=-√3/2时,f(x)min=-7/4 当x=1/2时,f(x)max=(2-√3)/4 (2) f(x)=x+2sina x-1=(x+sina)-1-sina ∴f(x)在(-∞,-sina)单调减,(-sina,+∞)单调增 要满足f(x)在[-√3/2,1/2]单调 则1/2