求证(tan(2π-θ)sin(2π-θ)cos(6π-θ))/((-cosθ)sin(5π+θ))=tanθ

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求证(tan(2π-θ)sin(2π-θ)cos(6π-θ))/((-cosθ)sin(5π+θ))=tanθ
求证(tan(2π-θ)sin(2π-θ)cos(6π-θ))/((-cosθ)sin(5π+θ))=tanθ

求证(tan(2π-θ)sin(2π-θ)cos(6π-θ))/((-cosθ)sin(5π+θ))=tanθ
利用诱导公式.
tan(2π-θ)=tanθ,sin(2π-θ)=-sinθ,cos(6π-θ)=cosθ,sin(5π-θ)=sinθ
所以:左边=[tanθ(-sinθ)cosθ]/[(-cosθ)sinθ]=tanθ=右边

tan(2π-θ)sin(-2π-θ)cos(6π-θ)/cos(θ+π)sin(5π+θ)
=(-tanθ)(-sinθ)cosθ)/(-cosθ)(-sinθ)
=tanθsinθcosθ/sinθcosθ
=tanθ

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