sin(2π-α)tan(α+3π)tan(-α-π)/tan(α-3π)cos(π-α)

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sin(2π-α)tan(α+3π)tan(-α-π)/tan(α-3π)cos(π-α)sin(2π-α)tan(α+3π)tan(-α-π)/tan(α-3π)cos(π-α)sin(2π-α)t

sin(2π-α)tan(α+3π)tan(-α-π)/tan(α-3π)cos(π-α)
sin(2π-α)tan(α+3π)tan(-α-π)/tan(α-3π)cos(π-α)

sin(2π-α)tan(α+3π)tan(-α-π)/tan(α-3π)cos(π-α)
[sin(2π-α)tan(3π+α)tan(-π-α)]/[cos(π-α)tan(α-3π)]
=[-sinα×tanα×(-tαna)]/[-cosα×(-tanα)]
=(sinα×tan^2 α)/[-cosα×(-sinα/cosα)]
=sinαxtan^2 α/sinα
=tan^2 α

sin(2π-α)=-sin(α-2π)=-sinα
tan(α+3π)=tanα
tan(-α-π)=tan(-α)=-tanα
tan(α-3π)=tanα
cos(π-α)=-cosα
上面五个量带入得到
原式=-(tanα)^2

答案为tan²α

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