3sin²a+2sin²b=2sin a,则sin²a+sin²b的取值范围是?
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![3sin²a+2sin²b=2sin a,则sin²a+sin²b的取值范围是?](/uploads/image/z/812354-50-4.jpg?t=3sin%26sup2%3Ba%EF%BC%8B2sin%26sup2%3Bb%EF%BC%9D2sin+a%2C%E5%88%99sin%26sup2%3Ba%EF%BC%8Bsin%26sup2%3Bb%E7%9A%84%E5%8F%96%E5%80%BC%E8%8C%83%E5%9B%B4%E6%98%AF%3F)
3sin²a+2sin²b=2sin a,则sin²a+sin²b的取值范围是?
3sin²a+2sin²b=2sin a,则sin²a+sin²b的取值范围是?
3sin²a+2sin²b=2sin a,则sin²a+sin²b的取值范围是?
因为3sin²a+2sin²b=2sin a,即有2sin²a+2sin²b=2sin a-sin²a,
于是sin²a+sin²b=sin a-(sin²a)/2=-(sina-1)²/2+1/2
所以sin²a+sin²b的取值范围是【-1/2,1/2]
2sina^2+2sinb^2 = 2sina-sina^2 = -(sina-1)^2 +1 因为sina在[-1,1]范围内,所以-(sina-1)^2 +1 在[-3,1]范围,所以sina^2+sin^b取植范围为[-3/2,1/2]