When the terms in a trig proof are being added or subtracted, you may create fractions where none were before. This is especially true when dealing with secant and cosecant, because you create fractions when you convert them (respectively) to

The same is true for tangent when you change it to

and cotangent becomes

Here’s an example that illustrates this point. Follow these steps to prove that

1. Convert all the trig functions to sines and cosines.

On the left side, you now have

2. Find the lowest common denominator of the two fractions.

This multiplication gives you