若α+β=2/3π,则sin^2α+sin^2β的取值范围

问题描述:

若α+β=2/3π,则sin^2α+sin^2β的取值范围

α+β=2/3π,2α+2β=4/3π,则2α=(4/3π)-2β
sin^2α+sin^2β=1-(cos2α+cos2β)/2
=1-[cos(4/3π-2β)+cos2β]/2
=1-[cos(-π/3+2β)]/2
-1=