若sin^2x+2sin^2y=2cosx,求y=sin^2x+sin^2y的取值范围

若sin^2x+2sin^2y=2cosx,求y=sin^2x+sin^2y的取值范围
若sin^2x+2sin^2y=2cosx,求y=sin^2x+sin^2y的取值范围

若sin^2x+2sin^2y=2cosx,求y=sin^2x+sin^2y的取值范围
由sin^2x+2sin^2y=2cosx得sin^2y=cosx-1/2sin^2x,所以y=sin^2x+sin^2y=sin^2x+cosx-1/2sin^2x=1/2sin^2x+cosx
然后把sin^2x转化为cosx,变成关于cosx的二元方程,而cosx的范围是-1到1,最后得出y的取值范围.