IMO Shortlist 1966 problem 9
Dodao/la:
arhiva2. travnja 2012. Find
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
such that trigonometric
![\frac{\sin 3x \cos (60^\circ -x)+1}{\sin(60^\circ - 7x) - \cos(30^\circ + x) + m}=0](/media/m/0/c/a/0ca683207368d7612ad32729ee4821b9.png)
where
![m](/media/m/1/3/6/1361d4850444c055a8a322281f279b39.png)
is a fixed real number.
%V0
Find $x$ such that trigonometric
$$\frac{\sin 3x \cos (60^\circ -x)+1}{\sin(60^\circ - 7x) - \cos(30^\circ + x) + m}=0$$
where $m$ is a fixed real number.
Izvor: Međunarodna matematička olimpijada, shortlist 1966