已知f（α）=sin(π-α)cos(2π-α)sin(π2-α)cos(-π-α)cos(π2-α)（1）化简f（α）；（2）当α=π3时，求f（α）的值．

Question

已知f（α）=(sin(π-α)cos(2π-α)sin((π)/(2)-α))/(cos(-π-α)cos((π)/(2)-α))
（1）化简f（α）；
（2）当α=(π)/(3)时，求f（α）的值．

Answer 1

（1）f（α）=(sin(π-α)cos(2π-α)sin((π)/(2)-α))/(cos(-π-α)cos((π)/(2)-α))=(sinαcosαcosα)/(-cosαsinα)=-cosα，
（2）当α=(π)/(3)时，f（(π)/(3)）=-cos(π)/(3)=-(1)/(2)．