化简1/( tan3α-tanα) -1/(cot3α-cotα)

1/(tan3α-tanα)-1/(cot3α-cotα)
=1/(sin3α/cos3α-sinα/cosα)-1/(cos3α/sin3α-cosα/sinα)
=(cos3αcosα)/(sin3αcosα-sinαcos3α)-(sin3αsinα)/(cos3αsinα-cosαsin3α)
=(cos3αcosα)/(sin2α)-(sin3αsinα)/sin(-2α)
=(cos3αcosα+sin3αsinα)/(sin2α)
=cos2α/(sin2α)
=cot2α