Graphing Trig Identities

To determine the validity of an identity by graphing, one must graph each side of the given equation in y=. According to the Transitive property, if an identity both graphs would be equal. To determine if

(sinx) - (cosx) = (sinx) + (cosx) 

Is an identity, we plug each side into the calculator like this:

But we get this graph:

Which shows that the equations above is not an identity.
Now let's graphically prove the hypothetical identity

 cot(x)/sec(x)=csc(x)-sin(x)

First we plug in the left hand side, which graphs as red:

Then the right hand side, which graphs in blue- if we are unable to see anymore red, the equation is an identity. 

Though it is helpful, one cannot prove an identity using only graphing. Trig proofs are an algebraic process where one can prove a statement by setting right side exactly equal to left side. Graphing can present errors in inputting correct values as well as this: if an equation is slightly different and looks very similar on a graph, it is easy to mistake it for an identity. Ideally, one would use both graphing and algebra to determine the validity of the identity.