Question

已知sinx+siny=1/3,求u=sinx-cos^2y的最值

Answer 1

sinx+siny=1/3 sinx=1/3-siny

(siny)^2+(cosy)^2=1 (cosy)^2=1-(siny)^2

u=sinx-cos^2y

u=(1/3-siny)-[1-(siny)^2]

u=(siny)^2-siny-2/3

u=(siny-1/2)^2-11/12

-1