$\sin 6\theta + \sin 4\theta + \sin 2\theta = 0,$ then $\theta = $
$\frac{{n\pi }}{4}$ or $n\pi \pm \frac{\pi }{3}$
$\frac{{n\pi }}{4}$ or $n\pi \pm \frac{\pi }{6}$
$\frac{{n\pi }}{4}$ or $2n\pi \pm \frac{\pi }{6}$
None of these
The solution of $3\tan (A - {15^o}) = \tan (A + {15^o})$ is
The number of solutions of $tan\, (5\pi\, cos\, \theta ) = cot (5 \pi \,sin\, \theta )$ for $\theta$ in $(0, 2\pi )$ is :
Let $P = \left\{ {\theta :\sin \,\theta - \cos \,\theta = \sqrt 2 \,\cos \,\theta } \right\}$ and $Q = \left\{ {\theta :\sin \,\theta + \cos \,\theta = \sqrt {2\,} \sin \,\theta } \right\}$ be two sets. Then
The value of the expression
$\frac{{\left (sin 36^o + cos 36^o - \sqrt 2 sin 27^o)( {\sin {{36}^0} + \cos {{36}^0} - \sqrt 2 \sin {{27}^0}} \right)}}{{2\sin {{54}^0}}}$ is less than
If $m$ and $n$ respectively are the numbers of positive and negative value of $\theta$ in the interval $[-\pi, \pi]$ that satisfy the equation $\cos 2 \theta \cos \frac{\theta}{2}=\cos 3 \theta \cos \frac{9 \theta}{2}$, then $mn$ is equal to $.............$.