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f(x)=(sin2x+2cos²x)/cosx
=(2sinxcosx+2cos²x)/cosx
=2cosx(sinx+cosx)/cosx
=2√2sin(x+π/4)·cosx/cosx
定义域分母≠0→x≠2kπ±π/2
∴f(x)可以化简为:f(x)=2√2sin(x+π/4) x≠2kπ±π/2
f(π/4)=2√2sin(π/4+π/4)=2√2
②将x+π/4看成整体:
单调递增区间:2kπ-π/2<x+π/4<2kπ+π/2→2kπ-3π/4<x<2kπ+π/4
对照所给区间x∈(0,π/2),f(x)的单调递增区间是x∈(0,π/4)
=(2sinxcosx+2cos²x)/cosx
=2cosx(sinx+cosx)/cosx
=2√2sin(x+π/4)·cosx/cosx
定义域分母≠0→x≠2kπ±π/2
∴f(x)可以化简为:f(x)=2√2sin(x+π/4) x≠2kπ±π/2
f(π/4)=2√2sin(π/4+π/4)=2√2
②将x+π/4看成整体:
单调递增区间:2kπ-π/2<x+π/4<2kπ+π/2→2kπ-3π/4<x<2kπ+π/4
对照所给区间x∈(0,π/2),f(x)的单调递增区间是x∈(0,π/4)
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