If $\cos \theta + \sec \theta = \frac{5}{2}$, then the general value of $\theta $ is
$n\pi \pm \frac{\pi }{3}$
$2n\pi \pm \frac{\pi }{6}$
$n\pi \pm \frac{\pi }{6}$
$2n\pi \pm \frac{\pi }{3}$
The general value of $\theta $ satisfying ${\sin ^2}\theta + \sin \theta = 2$ is
Let $S=\{x \in R: \cos (x)+\cos (\sqrt{2} x)<2\}$, then
If ${\left( {\frac{{\sin \theta }}{{\sin \phi }}} \right)^2} = \frac{{\tan \theta }}{{\tan \phi }} = 3,$ then the value of $\theta $ and $\phi $ are
$\tan \,{20^o}\cot \,{10^o}\cot \,{50^o}$ is equal to
Let $S=\left\{\theta \in(0,2 \pi): 7 \cos ^{2} \theta-3 \sin ^{2} \theta-2\right.$ $\left.\cos ^{2} 2 \theta=2\right\}$. Then, the sum of roots of all the equations $x ^{2}-2\left(\tan ^{2} \theta+\cot ^{2} \theta\right) x +6 \sin ^{2} \theta=0$ $\theta \in S$, is$...$