# formula

• Dec 30th 2009, 06:16 AM
Dogod11
formula
Hello friends, I know, and there is this formula for the sum of sines:

$\displaystyle sin(\alpha) + sin(\beta) = 2sin( \displaystyle\frac{\alpha + \beta}{2} ) cos( \displaystyle\frac{\alpha - \beta}{2} )$

and there is one for the sum of cosines,

I wonder if there is a similar to this:

$\displaystyle tan(\alpha) + tan(\beta)$

greetings
• Dec 30th 2009, 06:36 AM
skeeter
Quote:

Originally Posted by Dogod11
Hello friends, I know, and there is this formula for the sum of sines:

$\displaystyle sin(\alpha) + sin(\beta) = 2sin( \displaystyle\frac{\alpha + \beta}{2} ) cos( \displaystyle\frac{\alpha - \beta}{2} )$

and there is one for the sum of cosines,

I wonder if there is a similar to this:

$\displaystyle tan(\alpha) + tan(\beta)$

greetings

$\displaystyle \tan{\alpha} \pm \tan{\beta} = \frac{\sin(\alpha \pm \beta)}{\cos{\alpha}\cos{\beta}}$
• Dec 30th 2009, 07:06 AM
Dogod11
thanks
• Dec 30th 2009, 07:28 AM
Quote:

Originally Posted by Dogod11
Hello friends, I know, and there is this formula for the sum of sines:

$\displaystyle sin(\alpha) + sin(\beta) = 2sin( \displaystyle\frac{\alpha + \beta}{2} ) cos( \displaystyle\frac{\alpha - \beta}{2} )$

and there is one for the sum of cosines,

I wonder if there is a similar to this:

$\displaystyle tan(\alpha) + tan(\beta)$

greetings

HI

$\displaystyle \frac{\sin \alpha\cos \beta \pm \cos \alpha \sin \beta}{\cos \alpha\cos \beta}=\frac{\sin (\alpha\pm \beta)}{\cos \alpha\cos \beta}$