The number of solutions $x$ of the equation $\sin \left(x+x^2\right)-\sin \left(x^2\right)=\sin x$ in the interval $[2,3]$ is
$0$
$1$
$2$
$3$
$\sum\limits_{r = 1}^{100} {\frac{{\tan \,{2^{r - 1}}}}{{\cos \,{2^r}}}} $ is equal to
If $\sqrt 2 \sec \theta + \tan \theta = 1,$ then the general value $\theta $ is
If $\tan m\theta = \tan n\theta $, then the general value of $\theta $ will be in
If $\sin \theta + \cos \theta = \sqrt 2 \cos \alpha $, then the general value of $\theta $ is
The general solution of $\sin x - 3\sin 2x + \sin 3x = $ $\cos x - 3\cos 2x + \cos 3x$ is