2y+ycosx=1+sinxsinx-ycosx=2y-1√(1+y²)sin(x﹣θ)=2y-1则：sin(x﹣θ)=(2y-1)/√(1+y²)显然，-1≤(2y-1)/√(1+y²)≤1即：(2y-1)²/(1+y²)≤1 (2y-1)²≤y²+1 3y²-4y≤0 y(3y-4)≤0得：0≤y≤4/3所以，值域为[0,4/3]故最大值为4/3
