已知3sin^2α+sin^2β=2sinα,求sin^2α+sin^2β的最大值
问题描述：
已知3sin^2α+sin^2β=2sinα,求sin^2α+sin^2β的最大值
答
3sin^2α+sin^2β=2sinα,sin^2β=2sinα-3sin^2α,所以sin^2α+sin^2β=sin^2α+2sinα-3sin^2α=-2sin^2α+2sinα,令sinα=t,t∈[-1,1]-2t^2+2t=-2(t-1/2)^2+1/2对称轴t=1/2在区间内,所以t=1/2时取最大值1/2,所以s...