# Tan^2(2x) and Tan(2x?)

1. Mar 10, 2015

### Tyrion101

Is the first a squared version of the other? I understand the trig function involved if it's just (2x) and tan is not squared.

2. Mar 10, 2015

### Staff: Mentor

No, I think what you're seeing is for twice the angle

Tan(2*theta)=tan(theta+theta)

3. Mar 10, 2015

### Staff: Mentor

Tan squared is in general not equal to tan of twice the angle.

4. Mar 10, 2015

### Tyrion101

But is it equal to: (2tanx/1-tan^2x)^2 is what I'm asking. I may have been unclear.

5. Mar 10, 2015

### symbolipoint

Use precise pure-text symbolism to remove all ambiguity. Using TEX would be better.

6. Mar 10, 2015

### symbolipoint

(2tanx/1-tan^2x)^2
Trying TEX on my own, might work badly:
$$(\frac{2tan(x)}{1-tan^2(x)})^2$$

I cannot think of any clever identity. Try breaking into sines and cosines.

7. Mar 10, 2015

### symbolipoint

Now I understand what you asked.
No, those two are generally not equal.

8. Mar 10, 2015

### Tyrion101

Ok thanks! I'm beginning to understand. I'm going to be glad when the trig identities homework is fini(finished in French.)

9. Mar 10, 2015

### Staff: Mentor

@Tyrion101, despite what others have said in this thread, yes, $\tan^2(2x)$ is the square of $\tan(2x)$.

Yes and no. $\tan^2(2x)$ means $[\tan(2x)]^2$, which in turn is equal to $[\frac{2 \tan(x)}{1 - \tan^2(x)} ]^2$

In what you wrote, you are missing parentheses around the quantity in the denominator, 1 - tan2(x). What you wrote is the same as $\frac{2\tan(x)}{1} - \tan^2(x)$

10. Mar 10, 2015

### symbolipoint

... and should be clear by now.
It be nice to know your history about your studies of Trigonometry, Tyrion101. Nothing wrong in studying Algebra 2 and Trigonometry more than once each, and one does not need to enroll in a class to do that. One should expect to learn material better through repeated study.

11. Mar 10, 2015

### Tyrion101

Sorry for not completing the formula but I got my question answered. I get confused easily when frustrated or nervous, and in this case it was a bit of frustration. My two biggest problems in any math class seem to be the slowness at which I arrive at an answer, usually brought about by the other problem I have of misreading the question to begin with, I've long suspected that I have some form of dyslexia. For instance I saw a problem with -5beta (the actual symbol) and misread it to mean: -5/beta. Is there a at I can minimize this from happening?

12. Mar 10, 2015

### Staff: Mentor

I'm not an expert on dyslexia or related problems, but if you misread 5β as 5/β, maybe you need glasses or contacts. That doesn't sound like dyslexia to me.

Also, before you get started working a problem, go back over the problem description to make sure that your first reading of it was correct.

13. Mar 10, 2015

### Staff: Mentor

14. Mar 10, 2015

### Tyrion101

It's other things too, like I'll do a problem 20 times only to find out that there is no sine2x at all. It's very frustrating. From what I understand from having gone to a school that helped dyslexic and add or adhd kids, it seems somewhat similar, but as you say Mark it might not be dyslexia related at all. Thanks for the link on math dyslexia I'd never heard of it before.

15. Mar 10, 2015

### Staff: Mentor

As Sherlock Holmes might say:

We look but we don't not see.

You need to develop the over mind idea where as you're doing the problem you are looking over and validating what you did as you do it.

You can imagine yourself talking to yourself as you're doing the problem repeating what you're writing like you're teaching yourself.

Initially it may be hard to do and so it will take some practice to master.

Do you have someone you can teach to? By teaching you improve your learning skill.