(SIN X*COS X)/(1+SIN X+COS X)的值域?

来源：学生作业帮助网编辑：作业帮时间：2024/04/30 19:47:11

(SIN X*COS X)/(1+SIN X+COS X)的值域?
(SIN X*COS X)/(1+SIN X+COS X)的值域?

(SIN X*COS X)/(1+SIN X+COS X)的值域?
设SIN X+COS X=p
则SIN X*COS X=(p^2-1)/2(上式两边平方)
原式=(p^2-1)/(2(1+p))=(p-1)/2
其中,-根号2

设sin（x）+cos（x）=t
sin（x）*cos（x)=(t²-1)/2
f(x)=(t-1)(t+1)/[2(t+1)]=(t-1)/2
因为t∈【-√2，√2】
所以f(x)∈【﹙-1-√2﹚/2，（-1+√2）/2】
PS：如有错误敬请指出。

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