The number of solutions that the equation $sin5\theta cos3\theta = sin9\theta cos7\theta $ has in $\left[ {0,\frac{\pi }{4}} \right]$ is
$4$
$5$
$6$
$7$
The number of solutions of the equation $2 \theta-\cos ^{2} \theta+\sqrt{2}=0$ is $R$ is equal to
$sin 3\theta = 4 sin\, \theta \,sin \,2\theta \,sin \,4\theta$ in $0\, \le \,\theta\, \le \, \pi$ has :
The number of points in $(-\infty, \infty)$, for which $x^2-x \sin x-\cos x=0$, is
The solution of the equation $4{\cos ^2}x + 6$${\sin ^2}x = 5$
If $tan(\pi sin \theta)$ $= cot(\pi cos \theta)$, then $\left| {\cot \left( {\theta - \frac{\pi }{4}} \right)} \right|$ is -