f(x)=根号3 sin2x+2sin（兀／4+X - 知识问答

f(x)=根号3 sin2x+2sin（兀／4+X）cos(兀／4+x）

1个回答

sin（π/2+α）= cosα
f(x)=√3sin2x+2sin(π/4+x)cos(π/4+x)
=√3sin2x+sin(π/2+2x)
=√3sin2x+cos2x
=2(√3/2sin2x+1/2cos2x)
=2(sin2xcosπ/6+cos2xsinπ/6)
=2sin(2x+π/6)
T=2π/2=π
x∈[0,π/2]
2x∈[0,π]
2x+π/6∈[π/6,5π/6]
sin(2x+π/6)∈[-1/2,1]

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