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求函数f(x)=(sin2x-cos2x+1)/2sinx 的值域
人气:433 ℃ 时间:2019-10-19 16:07:35
解答
f(x)=(sin2x-cos2x+1)/2sinx
=(2sinxcosx-1+2sin²x+1)/2sinx
=sinx+cosx (x≠kπ)
=√2sin(x+π/4)
-√2≤f(x)≤√2,且f(x)≠1
值域=[-√2,1)∪(1,√2]
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