论文部分内容阅读
题:求函数y=(sinx+1/sin~2x)+(cos~2x+1/cos~2x)的极值。下面给出两个解答: 解一■解二∵sin~2x+cos~2x=1 ∴1/sin~2x+1/cos~2x=1/sin~2xcos~2x =4/sin~22x≥4 ∴y_(min)=5. 显然,两个答案不可能都正确。那么,究竟谁是谁非呢? 注意:式子sin~2x+1/sin~2x≥2,当且仅当x=kπ+n/2时等号才成立,而此时1/cos~2x不存在;式子cos~2x+1/cos~2≥2当且仅当x=kπ时
Question: Find the extremum of the function y=(sinx+1/sin~2x)+(cos~2x+1/cos~2x). Two solutions are given below: Solution One ■ Solution Two sin~2x+cos~2x=1 ∴1/sin~2x+1/cos~2x=1/sin~2xcos~2x =4/sin~22x≥4 ∴y_(min)=5. Obviously, both answers cannot be correct. So, who is right or wrong? Note: The formula sin~2x+1/sin~2x≥2, if and only if x=kπ+n/2, the equal sign only holds, and at this time 1/cos~2x Does not exist; Equation cos~2x+1/cos~2≥2 if and only if x=kπ