Example 3--Page 2

All right. Looks good. We now just need to continue to combine the two terms to one term, and then we get:

We are almost done. Now we compare two sides of this identity, we see that left side has a factor of 3. Let's see if we can pull 3 out of left side. Yes, we can do that.

Because 

This is a hard problem, but if you catch our idea you should easily understand all the steps.

Most people will prove this problem in this way. We have another way to do this problem.

The second way to prove this problem might confuse you a little bit, but we believe it's good for you to know how powerful you are once you know our idea.

This time, we still do it from left to right. But not like the first way, we are not trying to make right equal to . Because if we don't know, or forget this formula, it could be hard for us. So we want to prove L = R directly.

Also in this way, we want to reduce the difference of operations first. In the first way we were trying to reduce the difference of angles first. Now, our goal is to combine all the terms on the left to one, which is reducing the difference of operations. Please note that is a simple function, but the other two are not. Although we can combine all of them together at once, we recommend you not to do so, because once we solve the difficult parts, others will be fine.