# Question #a2cb0

##### 1 Answer

Feb 5, 2016

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#

... add

#<=> 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.

q.e.d.