If $\left| {\cos \,\theta \,\left\{ {\sin \theta + \sqrt {{{\sin }^2}\theta + {{\sin }^2}\alpha } } \right\}\,} \right|\, \le k,$ then the value of $k$ is
$\sqrt {1 + {{\cos }^2}\alpha } $
$\sqrt {1 + {{\sin }^2}\alpha } $
$\sqrt {2 + {{\sin }^2}\alpha } $
$\sqrt {2 + {{\cos }^2}\alpha } $
If $0 < x < \pi $ and $\cos x + \sin x = \frac{1}{2}$,then $tan \,x$ is
If $\sin \theta + \cos \theta = m$ and $\sec \theta + {\rm{cosec}}\theta = n$, then $n(m + 1)(m - 1) = $
If $\sin \theta = \frac{{24}}{{25}}$ and $\theta $ lies in the second quadrant, then $\sec \theta + \tan \theta = $
If for real values of $x,\cos \theta = x + \frac{1}{x},$ then
If $\sin x + {\sin ^2}x = 1,$ then ${\cos ^8}x + 2{\cos ^6}x + {\cos ^4}x = $