3sin²a+2sin²b=2sin a,则sin²a+sin²b的取值范围是?

问题描述:

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]