求y=(sinx+2)(cosx+2)的值域

题目

求y=(sinx+2)(cosx+2)的值域
求y=(sinx+2)乘以(cosx+2)的值域

答案

y=(sinx+2)(cosx+2)=sinxcosx+2(sinx+cosx)+4=1/2sin2x+2√2sin(x+π/4)+4=-1/2cos(2x+π/2)+2√2sin(x+π/4)+4=-1/2(1-2sin(x+π/4)^2)+2√2sin(x+π/4)+4=sin(x+π/4)^2+2√2sin(x+π/4)+7/2=[sin(x+π/4)+√2]^2+...