1. ## trigonometry

Hi guys

2. Originally Posted by bahram
Hi guys
Just to clarify the problem, is this correct?

$\displaystyle cos(3a) - \frac{cos(7a)}{sin(7a)} + sin(3a) = tan (2a)$

3. is the question $\displaystyle \frac{{\cos3a}-{\cos7a}}{{sin7a}+{sin3a}} = {\tan2a}$

or

$\displaystyle {\cos3a}-{\frac{cos7a}{\sin7a}}+{\sin3a} = {\tan2a}$?

Your syntax is a little unclear.

Either way you may find this indentity useful: $\displaystyle {\sin3a} = {\sin (a + 2a)}$ this also applies for cos and tan.

4. Originally Posted by bahram
Hi guys
$\displaystyle \frac{\cos(3a) - \cos(7a)}{\sin(7a) + \sin(3a)} =$

$\displaystyle \frac{\cos(5a - 2a) - \cos(5a + 2a)}{\sin(5a + 2a) + \sin(5a - 2a)} =$

$\displaystyle \frac{\cos(5a)\cos(2a) + \sin(5a)\sin(2a) - [\cos(5a)\cos(2a) - \sin(5a)\sin(2a)]}{\sin(5a)\cos(2a) + \cos(5a)\sin(2a) + \sin(5a)\cos(2a) - \cos(5a)\sin(2a)} =$

$\displaystyle \frac{2\sin(5a)\sin(2a)}{2\sin(5a)\cos(2a)} =$

$\displaystyle \frac{\sin(2a)}{\cos(2a)} = \tan(2a)$

5. ## hi

thanks skeeter. it's the best one