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
$2$
$3$
$5$
$6$
Let $S=\{x \in R: \cos (x)+\cos (\sqrt{2} x)<2\}$, then
The number of solutions of the equation $1 + {\sin ^4}\,x = {\cos ^2}\,3x,x\,\in \,\left[ { - \frac{{5\pi }}{2},\frac{{5\pi }}{2}} \right]$ is
The only value of $x$ for which ${2^{\sin x}} + {2^{\cos x}} > {2^{1 - (1/\sqrt 2 )}}$ holds, is
If sum of all the solutions of the equation $8\cos x \cdot \left( {\cos \left( {\frac{\pi }{6} + x} \right) \cdot \cos \left( {\frac{\pi }{6} - x} \right) - \frac{1}{2}} \right) = 1$ in $\left[ {0,\pi } \right]$ is $k\pi $then $k$ is equal to :
If $cosx + secx =\, -2$, then for a $+ve$ integer $n$, $cos^n x + sec^n x$ is