已知f(α)=(sin(Π／2-α)cos(2Π-α)tan(-α+3Π))／(tan(Π+α)sin(Π／2＋α)),化简f(α)

已知f(α)=(sin(Π／2-α)cos(2Π-α)tan(-α+3Π))／(tan(Π+α)sin(Π／2＋α)),化简f(α)
已知f(α)=(sin(Π／2-α)cos(2Π-α)tan(-α+3Π))／(tan(Π+α)sin(Π／2＋α)),化简f(α)

已知f(α)=(sin(Π／2-α)cos(2Π-α)tan(-α+3Π))／(tan(Π+α)sin(Π／2＋α)),化简f(α)
f(α)=(sin(Π／2-α)cos(2Π-α)tan(-α+3Π))／(tan(Π+α)sin(Π／2＋α))
=-cos(α)cos(α)tan(α)／(tan(α)cos(α))
=-cos(α)

答案：-cos(x)
求解过程：matlab代码实现
syms x;
f=(sin(pi/2-x)*cos(2*pi-x)*tan(-x+3*pi))/(tan(pi+x)*sin(pi/2+x));
g = simple(f)