How do you prove the identity 1 / (1- cosx) + 1/ (1+ cosx) = 2 csc^2x?

Working with the left hand side
##((1+cosx)+(1-cosx))/((1-cosx)(1+cosx))##
##(1+cosx+1-cosx)/(1-cos^2x)##
##2/sin^2x##
##2csc^2x##
which is equal to the right hand side