If $\sqrt 3 \cos \,\theta + \sin \theta = \sqrt 2 ,$ then the most general value of $\theta $ is
$n\pi + {( - 1)^n}\frac{\pi }{4}$
${( - 1)^n}\frac{\pi }{4} - \frac{\pi }{3}$
$n\pi + \frac{\pi }{4} - \frac{\pi }{3}$
$n\pi + {( - 1)^n}\frac{\pi }{4} - \frac{\pi }{3}$
If $\cot \theta + \tan \theta = 2{\rm{cosec}}\theta $, the general value of $\theta $ is
The number of solutions of the equation $2 \theta-\cos ^{2} \theta+\sqrt{2}=0$ is $R$ is equal to
If $\frac{{\tan 3\theta - 1}}{{\tan 3\theta + 1}} = \sqrt 3 $, then the general value of $\theta $ 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
The number of solutions of the equation $1 + {\sin ^4}\,x = {\cos ^2}\,3x,x\,\in \,\left[ { - \frac{{5\pi }}{2},\frac{{5\pi }}{2}} \right]$ is