已知x∈【0,π】,若sin(π/3-x)=1/5,则tan(7π/6+x)=

已知x∈【0,π】,若sin(π/3-x)=1/5,则tan(7π/6+x)=
已知x∈【0,π】,若sin(π/3-x)=1/5,则tan(7π/6+x)=

已知x∈【0,π】,若sin(π/3-x)=1/5,则tan(7π/6+x)=
令π/3-x=θ,则x=π/3-θ,sinθ=1/5.
∵x∈[0,π]
∴θ∈[-2π/3,π/3]
∵sinθ=1/5>0.
∴θ∈[0,π/3],cosθ=2√6/5.
tan(7π/6+x)=tan(π/6+x)=tan(π/6+π/3-θ)=cotθ.=cosθ/sinθ=2√6.

2根号6.
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