Use the trigonometric identity that states
Typically, a mathematical proof follows a series of logical arguments to show that some theorem is true based on a set of axioms (one or more basic concepts that are assumed to be true).
If one can reach a logical conclusion based on an axiom, without committing any mathematical errors, then the theorem is "proven".
Let's start by assuming the following is true:
Looking at the right hand side of the equation, it is a difference of squares, and so it can be factored into the following:
Now, let's divide both sides by
And, now, let's divide both sides by
Let's separate the terms on the right hand side of the equation:
Finally, let's replace
Simplifying, we get:
Since we were able to logically show that the end result was true based on our initial assumption which was known to be true, it must be the case that
Note: This problem can also be worked in reverse!