In order to establish identity, we work on one side of the equation...

In order to establish identity, we work on one side of the equation to obtain the other one.  I think it is by convention that we begin with the left side.  But it might be just my style of working math.  So I work on the left side:


If I was working on both sides of the identity instead of following the rule of working on the left side only, I would obtain the results much faster: