If $x = \sin {130^o}\,\cos {80^o},\,\,y = \sin \,{80^o}\,\cos \,{130^o},\,\,z = 1 + xy,$which one of the following is true
$x > 0,\,\,y > 0,\,\,z > 0$
$x > 0,\,\,y < 0,\,\,0 < z < 1$
$x > 0,\,\,y < 0,\,\,z > 1$
$x < 0,\,\,y < 0,\,0 < z < 1$
The value of $\tan 81^{\circ}-\tan 63^{\circ}-\tan 27^{\circ}+\tan 9^{\circ}$ is
If $\alpha $ is a root of $25{\cos ^2}\theta + 5\cos \theta - 12 = 0$, $\pi /2 < \alpha < \pi $, then $\sin 2\alpha $ is equal to
If $A + B + C = \pi ,$ then ${\tan ^2}\frac{A}{2} + {\tan ^2}\frac{B}{2} + $${\tan ^2}\frac{C}{2}$ is always
$1 + \cos 2x + \cos 4x + \cos 6x = $
Number of values of $ x \in \left[ {0,2\pi } \right]$ satisfying the equation $cotx - cosx = 1 - cotx. cosx$