# Math Help - Need help with arctan

1. ## Need help with arctan

I have some problems calculating problems like:
arctan 2 + arctan 3 (answer cannot contain cyclometric functions)
arctan(1+sqrt(2)) + arctan(1-sqrt(2)) (answer cannot contain cyclometric functions)

Any hint would be appreciated.

2. Hello, Sabo!

I'll do the first one.

I assume you know: . $\tan(A + B) \:=\:\frac{\tan(A) + \tan(B)}{1-\tan(A)\tan(B)}$

Evaluate: . $\arctan 2 + \arctan 3$

Let: . $\theta \;=\;\arctan 2 + \arctan 3$

Then: . $\tan\theta \;=\;\tan\bigg[\arctan 2 + \arctan 3\bigg] \;=\;\frac{\tan(\arctan 2) + \tan(\arctan 3)}{1 - \tan(\arctan 2)\tan(\arctan 3)}$

. . . . . $\tan\theta \;=\;\frac{2+3}{1-2\cdot3} \;=\;\frac{5}{-5} \;=\;-1$

Therefore: . $\theta \;=\;\arctan(-1) \;=\;\begin{Bmatrix}\dfrac{3\pi}{4} + \pi n \\ \\[-3mm] 135^o + 180^on \end{Bmatrix}$

3. Ah, so simple. Well, it usually is, isn't it? =)

Thanks a lot!