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函数f(x)=2sinx(sinx+cosx)的单调增区间为
人气:223 ℃ 时间:2020-05-14 15:45:27
解答
f(x)=2sin²x+2sinxcosx =1-cos2x+sin2x =1+√2*(√2/2*sin2x-√2/2*cos2x) =1+√2*sin(2x-π/4)令2kπ-π/2≤2x-π/4≤2kπ+π/2得:kπ-π/8≤x≤kπ+3π/8所以单调递增区间为[kπ-π/8,kπ+3π/8...
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