If ${\tan ^2}\theta - (1 + \sqrt 3 )\tan \theta + \sqrt 3 = 0$, then the general value of $\theta $ is
$n\pi + \frac{\pi }{4},n\pi + \frac{\pi }{3}$
$n\pi - \frac{\pi }{4},n\pi + \frac{\pi }{3}$
$n\pi + \frac{\pi }{4},n\pi - \frac{\pi }{3}$
$n\pi - \frac{\pi }{4},n\pi - \frac{\pi }{3}$
The number of solutions of $|\cos x|=\sin x$, such that $-4 \pi \leq x \leq 4 \pi$ is.
The number of all possible triplets $(a_1 , a_2 , a_3)$ such that $a_1+ a_2 \,cos \, 2x + a_3 \, sin^2 x = 0$ for all $x$ is
If $2{\tan ^2}\theta = {\sec ^2}\theta ,$ then the general value of $\theta $ is
The number of values of $x$ in the interval $[0, 5\pi]$ satisfying the equation $3sin^2x\, \,-\,\, 7sinx + 2 = 0$ is
The equation $\sin x\cos x = 2$ has