If ${\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0$, then the general value of $\theta $ is
$n\pi + \frac{\pi }{4},n\pi + \frac{\pi }{3}$
$n\pi - \frac{\pi }{4},n\pi + \frac{\pi }{3}$
$n\pi + \frac{\pi }{4},n\pi - \frac{\pi }{3}$
$n\pi - \frac{\pi }{4},n\pi - \frac{\pi }{3}$
Number of solutions of $5$ $cos^2 \theta -3 sin^2 \theta + 6 sin \theta cos \theta = 7$ 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 -
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 equation in variable $\theta, 3 tan(\theta -\alpha) = tan(\theta + \alpha)$, (where $\alpha$ is constant) has no real solution, then $\alpha$ can be (wherever $tan(\theta - \alpha)$ & $tan(\theta + \alpha)$ both are defined)
Solve $\cos x=\frac{1}{2}$