If $\sqrt 3 \cos \,\theta + \sin \theta = \sqrt 2 ,$ then the most general value of $\theta $ is

  • A

    $n\pi + {( - 1)^n}\frac{\pi }{4}$

  • B

    ${( - 1)^n}\frac{\pi }{4} - \frac{\pi }{3}$

  • C

    $n\pi + \frac{\pi }{4} - \frac{\pi }{3}$

  • D

    $n\pi + {( - 1)^n}\frac{\pi }{4} - \frac{\pi }{3}$

Similar Questions

If $e ^{\left(\cos ^{2} x+\cos ^{4} x+\cos ^{6} x+\ldots \ldots \infty\right) \log _{e} 2}$ satisfies the equation $t ^{2}-9 t +8=0,$ then the value of $\frac{2 \sin x}{\sin x+\sqrt{3} \cos x}\left(0 < x < \frac{\pi}{2}\right)$ is

  • [JEE MAIN 2021]

The most general value of $\theta $ satisfying the equations $\sin \theta = \sin \alpha $ and $\cos \theta = \cos \alpha $ is

  • [IIT 1971]

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

  • [JEE MAIN 2022]

If $\sec x\cos 5x + 1 = 0$, where $0 < x < 2\pi $, then $x =$

  • [IIT 1963]

$\sin 6\theta + \sin 4\theta + \sin 2\theta = 0,$ then $\theta = $