The general solution of ${\sin ^2}\theta \sec \theta + \sqrt 3 \tan \theta = 0$ is
$\theta = n\pi + {( - 1)^{n + 1}}\frac{\pi }{3},\theta = n\pi ,n \in Z$
$\theta = n\pi ,n \in Z$
$\theta = n\pi + {( - 1)^{n + 1}}\frac{\pi }{3},n \in Z$
$\theta = \frac{{n\pi }}{2},n \in Z$
If $n$ is any integer, then the general solution of the equation $\cos x - \sin x = \frac{1}{{\sqrt 2 }}$ is
If $\cos \theta = \frac{{ - 1}}{2}$ and ${0^o} < \theta < {360^o}$, then the values of $\theta $ are
The number of values of $\alpha $ in $[0, 2\pi]$ for which $2\,{\sin ^3}\,\alpha - 7\,{\sin ^2}\,\alpha + 7\,\sin \,\alpha = 2$ , is
The number of real numbers $\lambda$ for which the equality $\frac{\sin (\lambda \alpha) \quad \cos (\lambda \alpha)}{\sin \alpha}=\lambda-1$,holds for all real $\alpha$ which are not integral multiples of $\pi / 2$ is
The number of solutions of the equation $2 \theta-\cos ^{2} \theta+\sqrt{2}=0$ is $R$ is equal to