（1）log327+lg110000+ln(ee)+log2(log216)+823-(1681)−14．（2）已知f(α)＝sin(α−3π)cos(2π−α)sin(α+π2)cos(−π−α)sin(π−α)，化简f（α）．

Question

（1）log327+lg(1)/(10000)+ln(e√(e))+log2(log216)+8(2)/(3)-((16)/(81))− (1)/(4)．
（2）已知f(α)＝(sin(α−3π)cos(2π−α)sin(α+(π)/(2)))/(cos(−π−α)sin(π−α))，化简f（α）．

Answer 1

（1）原式=log327+lg(1)/(10000)+ln(e√(e))+log2(log216)+8(2)/(3)-(3)/(2)+−(3)/(2)=3-4+2+4-(3)/(2)=5．
（2）f(α)＝(sin(α−3π)cos(2π−α)sin(α+(π)/(2)))/(cos(−π−α)sin(π−α))=((−sinα)cosα(−cosα))/((−cosα)sinα)=-cosα．