The solution of equation ${\cos ^2}\theta + \sin \theta + 1 = 0$ lies in the interval
$\left( { - \frac{\pi }{4},\frac{\pi }{4}} \right)$
$\left( {\frac{\pi }{4},\frac{{3\pi }}{4}} \right)$
$\left( {\frac{{3\pi }}{4},\frac{{5\pi }}{4}} \right)$
$\left( {\frac{{5\pi }}{4},\frac{{7\pi }}{4}} \right)$
The equation $5x^2+12x + 13 = 0$ and $ax^2+bx + c = 0$ have a common root, where $a,b,c$ are the sides of $\Delta ABC$,then find $\angle C$ ? .....$^o$
If $\cos p\theta = \cos q\theta ,p \ne q$, then
Number of solutions of $\sqrt {\tan \theta } = 2\sin \theta ,\theta \in \left[ {0,2\pi } \right]$ is equal to
If $\sin \theta + 2\sin \phi + 3\sin \psi = 0$ and $\cos \theta + 2\cos \phi + 3\cos \psi = 0$ , then the value of $\cos 3\theta + 8\cos 3\phi + 27\cos 3\psi = $
The value of $\theta $ lying between $0$ and $\pi /2$ and satisfying the equation
$\left| {\,\begin{array}{*{20}{c}}{1 + {{\sin }^2}\theta }&{{{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{1 + {{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{{{\cos }^2}\theta }&{1 + 4\sin 4\theta }\end{array}\,} \right| = 0$