已知函数f(x)=-1/2+(SIN5X/2)/(2SINX/2)将其化成COSX表示的式子.急!谢谢

f(x)=-1/2+(SIN5X/2)/(2SINX/2)
=[sin5x/2-sinx/2]/2sinx/2
=[sin(3x/2+x)-sin(3x/2-x)]/2sinx/2
=2(cos3x/2)sinx/2sinx/2
=2(cos3x/2)(2sinx/2)(cosx/2)/2sinx/2
=2(cos3x/2)(cosx/2)
=2*1/2[cos(3x/2+x/2)+cos(3x/2-x/2)]
=2*1/2(cos2x+cosx)
=cos2x+cosx
=2(cosx)^2+cosx-1