If both roots of quadratic equation ${x^2} + \left( {\sin \,\theta + \cos \,\theta } \right)x + \frac{3}{8} = 0$ are positive and distinct then complete set of values of $\theta $ in $\left[ {0,2\pi } \right]$ is
$\left( {\frac{\pi }{{12}},\frac{{5\pi }}{{12}}} \right)$
$\left( {\frac{{13\pi }}{{12}},\frac{{17\pi }}{{12}}} \right)$
$\left( {\frac{{7\pi }}{{12}},\frac{{11\pi }}{{12}}} \right)$
$\left( {\frac{{19\pi }}{{12}},\frac{{23\pi }}{{12}}} \right)$
If $S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\begin{array}{*{20}{c}}
0&{\cos {\mkern 1mu} x}&{ - \sin {\mkern 1mu} x}\\
{\sin {\mkern 1mu} x}&0&{\cos {\mkern 1mu} x}\\
{\cos {\mkern 1mu} x}&{\sin {\mkern 1mu} x}&0
\end{array}} \right| = 0} \right\},$ then $\sum\limits_{x \in S} {\tan \left( {\frac{\pi }{3} + x} \right)} $ is equal to
Find the principal and general solutions of the question $\tan x=\sqrt{3}$.
The number of solutions of the equation $x +2 \tan x =\frac{\pi}{2}$ in the interval $[0,2 \pi]$ is :
Number of solutions of the equation $2^x + x = 2^{sin \ x} + \sin x$ in $[0,10\pi ]$ is -
Let $\theta, 0 < \theta < \pi / 2$, be an angle such that the equation $x ^2+4 x \cos \theta+\cot \theta=0$ has equal roots for $x$. Then $\theta$ in radians is