# [SOLVED] tangent sum identity issue

• October 21st 2009, 03:05 PM
satis
[SOLVED] tangent sum identity issue
I've been working through a tanget sum identity problem and I've mostly got it, except I've got the signs reversed. I was curious if someone could point out the mistake I made. I apologize for how long this is. All assistance is appreciated.

Problem is
$tan(A+B)$
where
$sinA = \frac{-3}{5}$
is in QIII
and
$cosB = \frac{-1}{4}$
is in QII

sinA= $\frac{-3}{5}$ so the hypotenuse is 5, the oppose side is -3, making the adacent side 4. Thus tan(A) = $\frac{-3}{4}$.

for B, cosB= $\frac{-1}{4}$ so the hypotenuse is 4, the adjacent side -1, making the opposite side $\sqrt15$. Thus tan(b) = $\frac{\sqrt15}{-1}$ or just $-\sqrt15$.

The tangent sum identity is $\frac{tanA+tanB}{1-tanAtanB}$

Substituting in, I get
$\frac{\frac{-3}{4}+ -\sqrt15}{1-\frac{-3}{4}(-\sqrt15)}$

which is
$\frac{\frac{-3-4\sqrt15}{4}}{1-\frac{3\sqrt15}{4}}$
and then
$\frac{\frac{-3-4\sqrt15}{4}}{\frac{4-3\sqrt15}{4}}$
followed by
$\frac{-3-4\sqrt15}{4}*\frac{4}{4-3\sqrt15}$
and finally
$\frac{-3-4\sqrt15}{4-3\sqrt15}$

unfortunately, the answer would appear to be
$\frac{3-4\sqrt15}{4+3\sqrt15}$

Can someone please point out my mistake?
• October 21st 2009, 03:28 PM
skeeter
Quote:

Originally Posted by satis
I've been working through a tanget sum identity problem and I've mostly got it, except I've got the signs reversed. I was curious if someone could point out the mistake I made. I apologize for how long this is. All assistance is appreciated.

Problem is
$tan(A+B)$
where
$sinA = \frac{-3}{5}$
is in QIII
and
$cosB = \frac{-1}{4}$
is in QII

sinA= $\frac{-3}{5}$ so the hypotenuse is 5, the oppose side is -3, making the adacent side (negative) 4. Thus tan(A) = $\textcolor{red}{\frac{-3}{-4}}$.