The general value $\theta $ is obtained from the equation $\cos 2\theta = \sin \alpha ,$ is
$2\theta = \frac{\pi }{2} - \alpha $
$\theta = 2n\pi \pm \left( {\frac{\pi }{2} - \alpha } \right)$
$\theta = \frac{{n\pi + {{( - 1)}^n}\alpha }}{2}$
$\theta = n\pi \pm \left( {\frac{\pi }{4} - \frac{\alpha }{2}} \right)$
The numbers of solution $(s)$ of the equation $\left( {1 - \frac{1}{{2\,\sin x}}} \right){\cos ^2}\,2x\, = \,2\,\sin x\, - \,3\, + \,\frac{1}{{\sin x}}$ in $[0,4\pi ]$ is
If $\tan m\theta = \tan n\theta $, then the general value of $\theta $ will be in
The most general value of $\theta $ satisfying the equations $\tan \theta = - 1$ and $\cos \theta = \frac{1}{{\sqrt 2 }}$ is
If $\cos {40^o} = x$ and $\cos \theta = 1 - 2{x^2}$, then the possible values of $\theta $ lying between ${0^o}$ and ${360^o}$is
The number of all possible triplets $(a_1 , a_2 , a_3)$ such that $a_1+ a_2 \,cos \, 2x + a_3 \, sin^2 x = 0$ for all $x$ is