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
$\frac{\pi}{6}$ only
$\frac{\pi}{12}$ or $\frac{5 \pi}{12}$
$\frac{\pi}{6}$ or $\frac{5 \pi}{12}$
$\frac{\pi}{12}$ only
The total number of solution of $sin^4x + cos^4x = sinx\, cosx$ in $[0, 2\pi ]$ is equal to
If $\sin {\rm{ }}\left( {\frac{\pi }{4}\cot \theta } \right) = \cos {\rm{ }}\left( {\frac{\pi }{4}\tan \theta } \right)\,\,,$ then $\theta = $
If $\cos \theta = \frac{{ - 1}}{2}$ and ${0^o} < \theta < {360^o}$, then the values of $\theta $ are
General solution of $eq^n\, 2tan\theta \, -\, cot\theta =\, -1$ is
If $0\, \le \,x\, < \frac{\pi }{2},$ then the number of values of $x$ for which $sin\,x -sin\,2x + sin\,3x=0,$ is