For $n \in Z$ , the general solution of the equation

$(\sqrt 3  - 1)\,\sin \,\theta \, + \,(\sqrt 3  + 1)\,\cos \theta \, = \,2$ is

  • A

    $\theta \, = \,2n\pi \, \pm \,\frac{\pi }{4}\, + \,\frac{\pi }{{12}}$

  • B

    $\theta \, = \,n\pi \, + {( - 1)^\pi }\,\frac{\pi }{4}\, + \,\frac{\pi }{{12}}$

  • C

    $\theta \, = \,2n\pi \, \pm \,\frac{\pi }{4}\, - \,\frac{\pi }{{12}}$

  • D

    $\theta \, = \,n\pi \, + {( - 1)^\pi }\,\frac{\pi }{4}\, - \,\frac{\pi }{{12}}$

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  • [JEE MAIN 2020]