函数y=sin²x-2sinxcosx-cos²x(x∈R)的单调区间为
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函数y=sin²x-2sinxcosx-cos²x(x∈R)的单调区间为
函数y=sin²x-2sinxcosx-cos²x(x∈R)的单调区间为
函数y=sin²x-2sinxcosx-cos²x(x∈R)的单调区间为
y=sin²x-2sinxcosx-cos²x
=-cos2x-sin2x
=-√2(√2/2cos2x+√2/2sin2x)
=-√2sin(2x+π/4)
1、当2kπ-π/2≤2x+π/4≤2kπ+π/2时(k∈Z),函数为单调增,区间为[kπ-3π/8,kπ+π/8]
2、当2kπ+π/2≤2x+π/4≤2kπ+3π/2时(k∈Z),函数为单调减,区间为[kπ+π/8,kπ+5π/4]
y=sin²x-2sinxcosx-cos²x=-(cos²x-sin²x)-2sinxcosx=-cos2x-sin2x=-√2sin(2x+π/4)
单调递增区间为〔-3π/8+kπ,π/8+kπ〕,单调递减区间为〔π/8+kπ,5π/8+kπ〕