# Thread: tan (A + B)

1. ## tan (A + B)

If A = arctan(2/3) and B = arctan(1/2), find tan (A + B).

2. Originally Posted by magentarita
If A = arctan(2/3) and B = arctan(1/2), find tan (A + B).
Hint:

$\tan{(\alpha + \beta)} = \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}$.

3. ## I know but...

Originally Posted by Prove It
Hint:

$\tan{(\alpha + \beta)} = \frac{\tan{\alpha} + \tan{\beta}}{1 - \tan{\alpha}\tan{\beta}}$.
I know this is the correct formula to use. My problem concerns the arctan values given. I also know that arctan means tangent inverse but how do I use the given arctan values in this formula?

4. $\tan{(\arctan{\theta})} = \theta$.

5. ## are you

Originally Posted by Prove It
$\tan{(\arctan{\theta})} = \theta$.
Are you saying that arctan(2/3) = 2/3 and that
arctan(1/2) = 1/2?

If that's the case, then A = 2/3 and B = 1/2. Is this what needs to plugged into the formula for tan (A + B)?

6. Originally Posted by magentarita
Are you saying that arctan(2/3) = 2/3 and that
arctan(1/2) = 1/2?

If that's the case, then A = 2/3 and B = 1/2. Is this what needs to plugged into the formula for tan (A + B)?
No. What he's saying is that $\tan\!\left(\arctan\!\left(\tfrac{2}{3}\right)\rig ht)=\tfrac{2}{3}$ and $\tan\!\left(\arctan\!\left(\tfrac{1}{2}\right)\rig ht)=\tfrac{1}{2}$.

Your $A$ and $B$ values are still those arctangent values, but when you substitute them into your identity, you take into consideration what ProveIt told you (and what I elaborated above).

7. ## can you

Originally Posted by Chris L T521
No. What he's saying is that $\tan\!\left(\arctan\!\left(\tfrac{2}{3}\right)\rig ht)=\tfrac{2}{3}$ and $\tan\!\left(\arctan\!\left(\tfrac{1}{2}\right)\rig ht)=\tfrac{1}{2}$.

Your $A$ and $B$ values are still those arctangent values, but when you substitute them into your identity, you take into consideration what ProveIt told you (and what I elaborated above).
Can you show me how this is done?

8. Originally Posted by magentarita
Can you show me how this is done?
$A = \arctan \left( \frac{2}{3} \right) \Rightarrow \tan A = \frac{2}{3}$.

$B = \arctan \left( \frac{1}{2} \right) \Rightarrow \tan B = \frac{1}{2}$.

9. ## ok

Originally Posted by mr fantastic
$A = \arctan \left( \frac{2}{3} \right) \Rightarrow \tan A = \frac{2}{3}$.

$B = \arctan \left( \frac{1}{2} \right) \Rightarrow \tan B = \frac{1}{2}$.
This is exactly what I thought.