Need help with arctan

**Sabo** · February 8th 2010, 06:30 PM

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.

**Soroban** · February 8th 2010, 08:54 PM

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

**Sabo** · February 8th 2010, 09:10 PM

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

Thanks a lot!

Thread: Need help with arctan

LinkBack

Thread Tools

Display

Need help with arctan

Similar Math Help Forum Discussions

arctan(y) = x^2 + C, y = ?

arctan

arctan(x)

Cot/Arctan

arctan(1/3)+arctan(1/2)

Search Tags