# Question #5060b

##### 1 Answer

Use the trigonometric identity that states

#### Explanation:

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:

Subtracting

Let's replace

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!