已知sina=3/2sin^2α+sin^2β,则函数y=sin^2α+sin^2β的值域为1
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已知sina=3/2sin^2α+sin^2β,则函数y=sin^2α+sin^2β的值域为1
已知sina=3/2sin^2α+sin^2β,则函数y=sin^2α+sin^2β的值域为
1
已知sina=3/2sin^2α+sin^2β,则函数y=sin^2α+sin^2β的值域为1
sina=3/2sin^2α+sin^2β
y=sin^2α+sin^2β=sin^2α+sina-3/2sin^2α=sina-1/2sin^2α
-1=
sina=3/2sin^2α+sin^2β
y=sin^2α+sin^2β=sin^2α+sina-3/2sin^2α=sina-1/2sin^2α
-1=<sina<=1
-1/2=<-1/2sin^2α<=0
-3/2=<y<=1
(-3/2,3/2)
y=sin^2α+sin^2β
=sin^2α+sina-3/2sin^2α
=sina-1/2sin^2α
=-1/2(sin^2α-sinα+1/4)+1/8
=-1/2(sinα-1/2)+1/8
因为-1《sinα《1
y(max)=1/8
y(min)=5/4
1/8《y《5/4
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