- Home
- Standard 11
- Mathematics
$\frac{{\sin 3\theta + \sin 5\theta + \sin 7\theta + \sin 9\theta }}{{\cos 3\theta + \cos 5\theta + \cos 7\theta + \cos 9\theta }} = $
$\tan 3\theta $
$\cot 3\theta $
$\tan 6\theta $
$\cot 6\theta $
Solution
(c) $\frac{{\sin \,\,3\theta + \sin \,\,5\theta + \sin \,7\theta + \sin 9\theta }}{{\cos 3\theta + \cos 5\theta + \cos \,7\theta + \cos \,9\theta }}$
$ = \frac{{(\sin \,3\theta + \sin \,9\theta ) + (\sin \,5\theta + \sin \,7\theta )}}{{(\cos \,3\theta + \cos \,9\theta ) + (\cos \,5\theta + \cos \,7\theta )}}$
$ = \frac{{2\,\sin \,6\theta \,\cos \,3\theta + 2\,\sin \,6\theta \,\cos \,\theta }}{{2\,\cos \,6\theta \,\cos \,3\theta + 2\,\cos \,6\theta \,\cos \,\theta }}$
$ = \frac{{2\,\sin \,6\theta \,(\cos \,3\theta + \cos \theta )}}{{2\,\cos \,6\theta \,(\cos \,3\theta + \cos \theta )}}$
$= \tan \,6\theta $.
