tan(5π-α)=3 求值sin(α-3π)+cos(π-α)/sin(-α)+cos(2π-α)

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tan(5π-α)=3求值sin(α-3π)+cos(π-α)/sin(-α)+cos(2π-α)tan(5π-α)=3求值sin(α-3π)+cos(π-α)/sin(-α)+cos(2π-α)ta

tan(5π-α)=3 求值sin(α-3π)+cos(π-α)/sin(-α)+cos(2π-α)
tan(5π-α)=3 求值sin(α-3π)+cos(π-α)/sin(-α)+cos(2π-α)

tan(5π-α)=3 求值sin(α-3π)+cos(π-α)/sin(-α)+cos(2π-α)
tan(5π-α)=3
tan(4π+π-α)=3
tan(π-α)=3
-tanα=3
tanα=-3
[sin(α-3π)+cos(π-α)]/[sin(-α)+cos(2π-α)]
=[sin(4π+α-3π)+cos(π-α)]/[sin(-α)+cosα]
=[sin(π+α)+cosα]/(sinα+cosα)
=(-sinα+cosα)/(sinα+cosα)
=(-sinα/cosα+cosα/cosα)/(sinα/cosα+cosα/cosα)
=(-tanα+1)/(tanα+1)
=[-(-3)+1]/(-3+1)
=4/(-2)
=-2