The solution of $\frac{1}{2} +cosx + cos2x + cos3x + cos4x = 0$ is
$x=\frac{2n\pi}{9},n\in I,n\neq 9m,m\in I$
$x=\frac{2n\pi}{9},n\in I,n= 9m,m\in I$
$x=\frac{n\pi}{9}+\frac{\pi}{2},n\in I$
$x=\frac{2n\pi}{3}+\frac{\pi}{6},n\in I$
Let $S\, = \,\left\{ {\theta \, \in \,[ - \,2\,\pi ,\,\,2\,\pi ]\, :\,2\,{{\cos }^2}\,\theta \, + \,3\,\sin \,\theta \, = \,0} \right\}$. Then the sum of the elements of $S$ is
The set of values of $x$ satisfying the equation,${2^{\tan \,\,\left( {x\,\, - \,\,{\textstyle{\pi \over 4}}} \right)}}$ $- 2$${\left( {0.25} \right)^{\frac{{{{\sin }^2}\,\left( {x\,\, - \,\,{\textstyle{\pi \over 4}}} \right)}}{{\cos \,\,2x}}}}$ $+ 1 = 0$, is :
The number of values of $x$ in the interval $\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)$ for which $14 \operatorname{cosec}^{2} x-2 \sin ^{2} x=21$ $-4 \cos ^{2} x$ holds, is
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 number of solutions of the equation $|\cot x|=\cot x+\frac{1}{\sin x}$ in the interval $[0,2 \pi]$ is