If $\cos 2\theta + 3\cos \theta = 0$, then the general value of $\theta $ is
$2n\pi \pm {\cos ^{ - 1}}\frac{{ - 3 + \sqrt {17} }}{4}$
$2n\pi \pm {\cos ^{ - 1}}\frac{{ - 3 - \sqrt {17} }}{4}$
$n\pi \pm {\cos ^{ - 1}}\frac{{ - 3 + \sqrt {17} }}{4}$
$n\pi \pm {\cos ^{ - 1}}\frac{{ - 3 - \sqrt {17} }}{4}$
One root of the equation $\cos x - x + \frac{1}{2} = 0$ lies in the interval
If $4{\sin ^2}\theta + 2(\sqrt 3 + 1)\cos \theta = 4 + \sqrt 3 $, then the general value of $\theta $ is
The equation $2{\cos ^2}\left( {\frac{x}{2}} \right)\,{\sin ^2}x\, = \,{x^2}\, + \,\frac{1}{{{x^2}}},\,0\,\, \leqslant \,\,x\,\, \leqslant \,\,\frac{\pi }{2}\,\,$ has
If $\tan \theta - \sqrt 2 \sec \theta = \sqrt 3 $, then the general value of $\theta $ is
The number of integral value $(s)$ of $'p'$ for which the equation $99\cos 2\theta - 20\sin 2\theta = 20p + 35$ , will have a solution is