Why did your answer get wrong first? You used the property of inequality, a? +b？ ≥2ab (if and only if a=b), let's look at the topic. When the equal sign holds, it is sinx=4/sinx, that is, sin? X=4, then can sinx be equal to 2? Yes, sinx is bounded. The maximum value can only be 1.
Answer the following positive questions. For a y=t+4/t function, the interval between [-2,0] and (0,2) is monotonically decreasing, and the other intervals are increasing (this part can be known through the derivative function, and if you are familiar with the "hook" function, you can know its monotonic interval at a glance).
If the minimum value is required, I think there should be another condition for this problem-sinx ∈ (0, 1) (otherwise, only the minimum value in the negative interval is negative infinity), then the interval (0, 1) is in the negative interval (0,2), so take the minimum value of 1 and answer.
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