# Thread: another simple question

1. ## another simple question

Hi people..
ok, this question is actually very simple and i did it 5 times but i didn't get the answer as provided.

here is the question..
A is in 3rd quadrant with cos A=-24/25 and B in the 2nd quadrant with cos B=-8/17. Find tan(A+B).

Answer:-304/297<<----- i believe that the answer provided is wrong!

can anybody prove that i'm wrong?
thanks in advance

2. ## Trigonometry

Hello lanzailan
Originally Posted by lanzailan
Hi people..
ok, this question is actually very simple and i did it 5 times but i didn't get the answer as provided.

here is the question..
A is in 3rd quadrant with cos A=-24/25 and B in the 2nd quadrant with cos B=-8/17. Find tan(A+B).

Answer:-304/297<<----- i believe that the answer provided is wrong!

can anybody prove that i'm wrong?
thanks in advance
$\tan A = \frac{7}{24}, \tan B = -\frac{15}{8}$

$\Rightarrow \tan (A+B) = \frac{\tan A + \tan B}{1 - \tan A \tan B}$

$= \left(\frac{7}{24} - \frac{15}{8}\right) \div \left(1 + \frac{7}{24}\times\frac{15}{8}\right)$

$= \frac{7\times 8 - 15 \times 24}{24 \times 8 + 7\times 15}$

$=-\frac{304}{297}$

Grandad

3. ok now i see where i did it wrong..
in 3rd quadrant tanA should be positive.

thanks Grandad