If ${\sin ^2}\theta - 2\cos \theta + \frac{1}{4} = 0,$ then the general value of $\theta $ is
$n\pi \pm \frac{\pi }{3}$
$2n\pi \pm \frac{\pi }{3}$
$2n\pi \pm \frac{\pi }{6}$
$n\pi \pm \frac{\pi }{6}$
Let $X=\{x \in R: \cos (\sin x)=\sin (\cos x)\} .$ The number of elements in $X$ is
The number of points in $(-\infty, \infty)$, for which $x^2-x \sin x-\cos x=0$, is
The smallest positive root of the equation $tanx\, -\, x = 0$ lies on
If $\cot \theta + \cot \left( {\frac{\pi }{4} + \theta } \right) = 2$, then the general value of $\theta $ is
If $sin\, \theta = sin\, \alpha$ then $sin\, \frac{\theta }{3}$ =