Problems:
verify the identity of trigonometry
(1) sinx/(1-cosx)=cscx+cotx, 0
(2)(cosx)2-(sinx)2-sin(2x)=((cos2x)2-(sin(2x)2)/(cos2x+sin2x)
(3)sin(pi/4-x)=sqrt(2)/2(cosx-sinx)
(4)sin(180-x+y)=sinxcosy-cosxsiny
(5)2sinxsin3x=(1-cos2x)(1+2cos2x)
(6)sinx-cos2x=(2sinx-1)(sinx+1).