由y=cos²x+2sinx-1/2=1-sin²x+2sinx-1/2=-sin²x+2sinx+1/2=-（sin²x-2sinx+1）+3/2=-（sinx-1）²+3/2∵x∈[π/6,5π/6],∴当x=π/2时,有最大值：f（π/2）=3/2,当x=π/6或x=5π/6,有最小值...