已知函数f(x)=sin2x(sinx+cosx)/cosx
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已知函数f(x)=sin2x(sinx+cosx)/cosx
A=2,T=π
∴ω=2
∴f(x)=2sin(2x+φ﹚
过﹙π/6,2﹚
∴2sin(π/3+φ﹚=2
sin(π/3+φ﹚=1
π/3+φ=2kπ+π/2
φ=2kπ+π/6
∴φ=π/6
∴f(x)=2sin(2x+π/6﹚
2x+π/6∈[2kπ-π/2,2kπ+π/2]
∴x∈[kπ-π/3,kπ+π/6],k∈Z
g(x)=2sin(2x+π/6﹚+2cos2x
=√3sin(2x﹚+3cos﹙2x﹚
=2√3sin(2x+π/3﹚
x∈[﹣π/6,π/4]
2x+π/3∈[0,5π/6]
∴sin﹙2x+π/3﹚∈[0,1]
g(x)∈[0,2√3]
∴ω=2
∴f(x)=2sin(2x+φ﹚
过﹙π/6,2﹚
∴2sin(π/3+φ﹚=2
sin(π/3+φ﹚=1
π/3+φ=2kπ+π/2
φ=2kπ+π/6
∴φ=π/6
∴f(x)=2sin(2x+π/6﹚
2x+π/6∈[2kπ-π/2,2kπ+π/2]
∴x∈[kπ-π/3,kπ+π/6],k∈Z
g(x)=2sin(2x+π/6﹚+2cos2x
=√3sin(2x﹚+3cos﹙2x﹚
=2√3sin(2x+π/3﹚
x∈[﹣π/6,π/4]
2x+π/3∈[0,5π/6]
∴sin﹙2x+π/3﹚∈[0,1]
g(x)∈[0,2√3]
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