The smallest positive values of $x$ and $y$ which satisfy $\tan (x - y) = 1,\,$ $\sec (x + y) = \frac{2}{{\sqrt 3 }}$ are
$x = \frac{{25\pi }}{{24}},\,y = \frac{{19\pi }}{{24}}$
$x = \frac{{37\pi }}{{24}},\,y = \frac{{7\pi }}{{24}}$
$x = \frac{\pi }{4},\,y = \frac{\pi }{2}$
$a$ or $b$ both
Let $S=\left\{\theta \in[-\pi, \pi]-\left\{\pm \frac{\pi}{2}\right\}: \sin \theta \tan \theta+\tan \theta=\sin 2 \theta\right\} \text {. }$ If $T =\sum_{\theta \in S } \cos 2 \theta$, then $T + n ( S )$ is equal
The number of solution of the equation,$\sum\limits_{r = 1}^5 {\cos (r\,x)} $ $= 0$ lying in $(0, \pi)$ is :
Values of $\theta (0 < \theta < {360^o})$ satisfying ${\rm{cosec}}\theta + 2 = 0$ are
The roots of the equation $1 - \cos \theta = \sin \theta .\sin \frac{\theta }{2}$ is
The solution of $\frac{1}{2} +cosx + cos2x + cos3x + cos4x = 0$ is