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有很多函数的最值或值域问题可转化为求二次函数的最值或值域问题,而二次函数的最值或值域问题一般有两类:一类是在实数范围内的最值或值域,一类是在某一区间上的最值或值域.对于后者,有的题目中区间没有明确告之,而是隐含在题目的条件内.如果不能充分挖掘题目的隐含条件,往往会影响结果的正确性. 例 1 若sin2α+2sin2β=2cosα,求sin2α+sin2β的最大值和最小值. 错解:由条件得sin2β=cosα-1/2(sin2α)
There are many functions with the most value or range problem that can be converted into the most value or range problem of the quadratic function. The problem of the quadratic function’s maximum value or value range generally has two types: one is the most in the real number range. Value or value domain, a category is the most value or range of values in a certain range. For the latter, some items in the range are not explicitly reported, but implicit in the conditions of the title. If you can not fully tap the topic Implicit conditions often affect the correctness of the results. Example 1 If sin2α+2sin2β=2cosα, find the maximum and minimum values of sin2α+sin2β. False solutions: sin2β=cosα-1/2(sin2α)