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
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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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