试题记F(a,θ)=a2+2asinθ+2/a2+2asinθ+2,对任意实数a,θ,函数.F(a,θ)的最大值与最小值之和是____.这是2012年南京师范大学附中高三最后一次模考试题,命题者匠心独运,将θ的正弦和余弦与a的二次齐次分式有机结合,编拟出的一个多变量函数的最值问题.这类试题能全面检测学生的数学素养和思维能力,是高考的热点,同时这类问题 The answer to this question is F (a, θ) = a2 + 2asinθ + 2 / a2 + 2asinθ + 2. For any real a, θ, the sum of the maximum and minimum values ​​of F In 2012 Nanjing Normal University Middle School Senior High School last model test questions, propositions originality, the θ sine and cosine and a quadratic homogeneous fraction, the most developed a multivariable function problem. Such questions can be a comprehensive test of students’ mathematical literacy and thinking ability, is a hot college entrance examination, while such problems