Hi guys
could you please help me to prove cos3a-cos7a/sin7a+sin3a=tan2a
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.
$\displaystyle \frac{\cos(3a) - \cos(7a)}{\sin(7a) + \sin(3a)} =$
$\displaystyle \frac{\cos(5a - 2a) - \cos(5a + 2a)}{\sin(5a + 2a) + \sin(5a - 2a)} =$
$\displaystyle \frac{\cos(5a)\cos(2a) + \sin(5a)\sin(2a) - [\cos(5a)\cos(2a) - \sin(5a)\sin(2a)]}{\sin(5a)\cos(2a) + \cos(5a)\sin(2a) + \sin(5a)\cos(2a) - \cos(5a)\sin(2a)} =$
$\displaystyle \frac{2\sin(5a)\sin(2a)}{2\sin(5a)\cos(2a)} = $
$\displaystyle \frac{\sin(2a)}{\cos(2a)} = \tan(2a)$