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
$\left( {\frac{\pi }{{12}},\frac{{5\pi }}{{12}}} \right)$
$\left( {\frac{{13\pi }}{{12}},\frac{{17\pi }}{{12}}} \right)$
$\left( {\frac{{7\pi }}{{12}},\frac{{11\pi }}{{12}}} \right)$
$\left( {\frac{{19\pi }}{{12}},\frac{{23\pi }}{{12}}} \right)$
The solution of the equation $\sec \theta - {\rm{cosec}}\theta = \frac{4}{3}$ is
If $\sec x\cos 5x + 1 = 0$, where $0 < x < 2\pi $, then $x =$
If $\sin x=\frac{3}{5}, \cos y=-\frac{12}{13},$ where $x$ and $y$ both lie in second quadrant, find the value of $\sin (x+y)$.
If $1\,\, + \,\,\sin \theta \,\, + \,\,{\sin ^2}\theta + \ldots .\,\,to\,\,\infty \,\, = \,\,4\, + 2\sqrt 3 ,\,\,0\,\, < \,\theta \,\,\pi ,\,\,\theta \,\, \ne \,\frac{\pi }{2}\,,$ then $\theta = $
If $2\,cos\,\theta + sin\, \theta \, = 1$ $\left( {\theta \ne \frac{\pi }{2}} \right)$ , then $7\, cos\,\theta + 6\, sin\, \theta $ is equal to