How do you verify sinx/(1-cosx) + (1-cosx)/sinx = 2cscx?

##sinx/(1-cosx)+(1-cosx)/sinx = 2cscx##
##sinx/(1-cosx)+(1-cosx)/sinx = [sin^2x+(1-cosx)^2]/[(1-cosx)sinx]##
## = [sin^2x+cos^2x+1-2cosx]/[(1-cosx)sinx]##
## = [1+1-2cosx]/[(1-cosx)sinx]##
## = [2-2cosx]/[(1-cosx)sinx]##
## = 2cancel[1-cosx]/[cancel(1-cosx)sinx]##
## = 2/sinx##
## = 2cscx##