Question

3sina^2+2cosb^2=2sina求sina^2+sin b^2范围

Answer 1

由原式可知

cosb^2=sina-3/2(sina^2)

所以

sinb^2=1-cosb^2=1-sina+3/2(sina^2)

=3/2(sina^2)-sina+1

所以所求

sina^2+sinb^2

=sina^2+3/2sina^2-sina+1

=5/2sina^2-sina+1

=5/2{[sina-(1/5)]^2}+1

所以原式属于

[1,23/5]