If $4{\sin ^2}\theta + 2(\sqrt 3 + 1)\cos \theta = 4 + \sqrt 3 $, then the general value of $\theta $ is
$2n\pi \pm \frac{\pi }{3}$
$2n\pi + \frac{\pi }{4}$
$n\pi \pm \frac{\pi }{3}$
$n\pi - \frac{\pi }{3}$
The general solution of $a\cos x + b\sin x = c,$ where $a,\,\,b,\,\,c$ are constants
The solution of $3\tan (A - {15^o}) = \tan (A + {15^o})$ is
The number of integral values of $k$, for which the equation $7\cos x + 5\sin x = 2k + 1$ has a solution, is
The number of distinct solutions of the equation $\frac{5}{4} \cos ^2 2 x+\cos ^4 x+\sin ^4 x+\cos ^6 x+\sin ^6 x=2$ in the interval $[0,2 \pi]$ is
If $tan(\pi sin \theta)$ $= cot(\pi cos \theta)$, then $\left| {\cot \left( {\theta - \frac{\pi }{4}} \right)} \right|$ is -