The number of elements in the set $S=$ $\left\{\theta \in[-4 \pi, 4 \pi]: 3 \cos ^{2} 2 \theta+6 \cos 2 \theta-\right.$ $\left.10 \cos ^{2} \theta+5=0\right\}$ is

  • [JEE MAIN 2022]
  • A

    $32$

  • B

    $33$

  • C

    $34$

  • D

    $35$

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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 smallest positive root of the equation $tanx\,  -\,  x = 0$ lies on

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
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  • [JEE MAIN 2017]

The solution of  $\frac{1}{2} +cosx + cos2x + cos3x + cos4x = 0$ is 

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