y=sinx+cos2x=-2sin²x+sinx+1=-2(sinx-1/4)²+9/8,因为x∈[π/6,3π/4],sinx∈[1/2,1],所以y∈[0,1]且当x=π/6时,y最大值=-2(1/2-1/4)²+9/8=1,当x=π/2时,y最小值=-2(1-1/4)²+9/8=0....