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
The general solution of the trigonometric equation $tan\, x + tan \,2x + tan\, 3x = tan \,x · tan\, 2x · tan \,3x$ is
Number of values of $x$ satisfying $2sin^22x = 2cos^28x + cos10x$ in $x \in \left[ { - \frac{\pi }{4},\frac{\pi }{4}} \right]$ is-
If $\tan m\theta = \tan n\theta $, then the general value of $\theta $ will be in
The equation ${\sin ^4}x + {\cos ^4}x + \sin 2x + \alpha = 0$ is solvable for
If the equation $2\ {\sin ^2}x + \frac{{\sin 2x}}{2} = k$ , has atleast one real solution, then the sum of all integral values of $k$ is