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 smallest positive angle which satisfies the equation $2{\sin ^2}\theta + \sqrt 3 \cos \theta + 1 = 0$, is
The equation $3\cos x + 4\sin x = 6$ has
The general solution of the equation $sin^{100}x\,-\,cos^{100} x= 1$ is
If $\sin \theta + \cos \theta = \sqrt 2 \cos \alpha $, then the general value of $\theta $ is
The value of $\theta $ satisfying the given equation $\cos \theta + \sqrt 3 \sin \theta = 2,$ is