The solution of equation ${\cos ^2}\theta + \sin \theta + 1 = 0$ lies in the interval
$\left( { - \frac{\pi }{4},\frac{\pi }{4}} \right)$
$\left( {\frac{\pi }{4},\frac{{3\pi }}{4}} \right)$
$\left( {\frac{{3\pi }}{4},\frac{{5\pi }}{4}} \right)$
$\left( {\frac{{5\pi }}{4},\frac{{7\pi }}{4}} \right)$
If $\cos \theta = - \frac{1}{{\sqrt 2 }}$ and $\tan \theta = 1$, then the general value of $\theta $ is
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
The equation $\sqrt 3 \sin x + \cos x = 4$ has
Number of solution$(s)$ of the equation $\sin 2\theta + \cos 2\theta = - \frac{1}{2},\theta \in \left( {0,\frac{\pi }{2}} \right)$ is-
Let $f(x) = \cos \sqrt {x,} $ then which of the following is true