If $3({\sec ^2}\theta + {\tan ^2}\theta ) = 5$, then the general value of $\theta $ is
$2n\pi + \frac{\pi }{6}$
$2n\pi \pm \frac{\pi }{6}$
$n\pi \pm \frac{\pi }{6}$
$n\pi \pm \frac{\pi }{3}$
Let $\theta, 0 < \theta < \pi / 2$, be an angle such that the equation $x ^2+4 x \cos \theta+\cot \theta=0$ has equal roots for $x$. Then $\theta$ in radians is
The smallest positive angle which satisfies the equation $2{\sin ^2}\theta + \sqrt 3 \cos \theta + 1 = 0$, is
The general solution of ${\sin ^2}\theta \sec \theta + \sqrt 3 \tan \theta = 0$ is
If $\tan (\pi \cos \theta ) = \cot (\pi \sin \theta )$, then $\sin \left( {\theta + \frac{\pi }{4}} \right)$ equals
If $2\,cos\,\theta + sin\, \theta \, = 1$ $\left( {\theta \ne \frac{\pi }{2}} \right)$ , then $7\, cos\,\theta + 6\, sin\, \theta $ is equal to