For $n \in Z$ , the general solution of the equation
$(\sqrt 3 - 1)\,\sin \,\theta \, + \,(\sqrt 3 + 1)\,\cos \theta \, = \,2$ is
$\theta \, = \,2n\pi \, \pm \,\frac{\pi }{4}\, + \,\frac{\pi }{{12}}$
$\theta \, = \,n\pi \, + {( - 1)^\pi }\,\frac{\pi }{4}\, + \,\frac{\pi }{{12}}$
$\theta \, = \,2n\pi \, \pm \,\frac{\pi }{4}\, - \,\frac{\pi }{{12}}$
$\theta \, = \,n\pi \, + {( - 1)^\pi }\,\frac{\pi }{4}\, - \,\frac{\pi }{{12}}$
If $\sin (A + B) =1 $ and $\cos (A - B) = \frac{{\sqrt 3 }}{2},$ then the smallest positive values of $A$ and $ B$ are
The number of values of $\alpha $ in $[0, 2\pi]$ for which $2\,{\sin ^3}\,\alpha - 7\,{\sin ^2}\,\alpha + 7\,\sin \,\alpha = 2$ , is
If $\sec 4\theta - \sec 2\theta = 2$, then the general value of $\theta $ is
Let $A=\left\{\theta \in R \mid \cos ^2(\sin \theta)+\sin ^2(\cos \theta)=1\right\}$ and $B=\{\theta \in R \mid \cos (\sin \theta) \sin (\cos \theta)=0\}$. Then, $A \cap B$
The general solution of ${\sin ^2}\theta \sec \theta + \sqrt 3 \tan \theta = 0$ is