I have to guess here but I'm assuming that you would like to prove the following identity:
#sin x / (1 - cos x) - (1 + cos x )/ sin x = 0#
Let's start by bringing the second fraction to the right-hand side:
#<=> sin x / (1 - cos x) = (1 + cos x)/ sin x #
Now, in order to get rid of the fractions, you should multiply both sides with both denominators:
#<=> sin x * sin x = (1 + cos x) * (1 - cos x)#
... make use of the formula
#<=> sin^2 x = 1^2 - cos^2 x#
#<=> sin^2 x + cos^2 x = 1#
However, this is a well-known identity.
As your original equation is equivalent to this identity and the identity certainly holds, your equation holds as well.