# Awkward Trig. Equation

• May 5th 2010, 09:58 PM
Deimos
Awkward Trig. Equation
Hello all. I have a trig problem here that I am not necessarily stuck on, but just wanted to confirm results with someone else.

Using the proof:

$\frac{\tan\alpha\pm\tan\beta}{1\mp\tan\alpha\tan\b eta}$

Where:

$\tan\alpha = \frac{3\sqrt5}{5}$
$\tan\beta = \frac{-\sqrt15}{4}$

For:

$\tan(\alpha+\beta)$

What do you get?
• May 5th 2010, 10:08 PM
pickslides
$\frac{4(3\sqrt{5}+\sqrt{15})}{16-3\sqrt{75}}$

Can be simplified further.
• May 5th 2010, 10:13 PM
Deimos
I made a mistake on $\tan\alpha$.

I meant to write:

$\tan\alpha = \frac{3\sqrt5}{5}$

I fixed the initial post as well. Sorry about that.
• May 6th 2010, 02:13 AM
Hello Deimos

With denominator rationalised, I get:
$\frac{(56\sqrt3-93)\sqrt5}{55}$
which checks out OK on my calculator.

I don't think that will simplify any further.