化简:[cos(α-5π)+2sin(3π-α)]/[csc(3π+α)+sec(5π+α)]

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化简:[cos(α-5π)+2sin(3π-α)]/[csc(3π+α)+sec(5π+α)]

化简:[cos(α-5π)+2sin(3π-α)]/[csc(3π+α)+sec(5π+α)]
化简:[cos(α-5π)+2sin(3π-α)]/[csc(3π+α)+sec(5π+α)]

化简:[cos(α-5π)+2sin(3π-α)]/[csc(3π+α)+sec(5π+α)]
[cos(α-5π)+2sin(3π-α)]/[csc(3π+α)+sec(5π+α)]
=[cosacos5π+sinasin5π+2(sin3πcosa-cos3πsina)]/[1/sin(3π+a)+1/cos(5π+a)]
=[-cosa+2sina]/[-1/sina-1/cosa]
=(-cosa+2sina)*sinacosa/(-cosa-sina)
=(-1+2tana)tana/(-1-tana)
=(tana-2tan²a)/(1+tana)

[cos(α-5π)+2sin(3π-α)]/[csc(3π+α)+sec(5π+α)]
=(-cosα+2sinα) / (-cscα-secα)
=(cosα-2sinα) / (cscα+secα)

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