若3sina^2+2sinb^2=2sina,求sina^2+sinb^2的取值范围?
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若3sina^2+2sinb^2=2sina,求sina^2+sinb^2的取值范围?
若3sina^2+2sinb^2=2sina,求sina^2+sinb^2的取值范围?
若3sina^2+2sinb^2=2sina,求sina^2+sinb^2的取值范围?
2(sin²a+sin²b)=-sin²a+2sina=-(sina-1)²+1
2sin²b=2sina-3sin²a
因为0
3sina^2+2sinb^2=2sina 则 显然sina》0 即0《sina《1
2sina^2+2sinb^2=2sina- sina^2
∴sina^2+sinb^2 =1/2(2sina- sina^2)=-1/2(sina-1)2+1/2
∴0《(sina-1)2《1
∴0《-1/2(sina-1)2+1/2《1/2
∴0《 sina^2+sinb^2《1/2
即取值范围为 大于等于0且小于等于1/2
3sina^2+2sinb^2=2sina
3(1-cosa^2)+ 2sinb^2=2sina
sinb^2= sina+3(cosa^2-1)/2
sina^2+sinb^2=sina^2+sina+3(cosa^2-1)/2
=sina^2+cosa^2+sina+cosa^2/2-3/2
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3sina^2+2sinb^2=2sina
3(1-cosa^2)+ 2sinb^2=2sina
sinb^2= sina+3(cosa^2-1)/2
sina^2+sinb^2=sina^2+sina+3(cosa^2-1)/2
=sina^2+cosa^2+sina+cosa^2/2-3/2
=-1/2+sina+cosa^2
=sina-(1-cosa^2)2
=sina-sina^2/2
=-(sina^2-2sina+1)/2+1/2
=-(sina-1)^2+1/2
因为 -1《sina《 1
又由题得知 sina》0
所以 0《sina《 1
-1《sina-1《 0
0《(sina-1)^2《 1
0 《-(sina-1)^2+1/2《 1/2
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