The value of $\left( {1 + \cos \frac{\pi }{9}} \right)\left( {1 + \cos \frac{{3\pi }}{9}} \right)\left( {1 + \cos \frac{{5\pi }}{9}} \right)\left( {1 + \cos \frac{{7\pi }}{9}} \right)$ is
$\frac{9}{{16}}\,$
$\frac{10}{{16}}\,$
$\frac{12}{{16}}\,$
$\frac{5}{{16}}\,$
Value of $\frac{{4\sin {9^o}\sin {{21}^o}\sin {{39}^o}\sin {{51}^o}\sin {{69}^o}\sin {{81}^o}}}{{\sin {{54}^o}}}$ is equal to
$\frac{{\sqrt 2 - \sin \alpha - \cos \alpha }}{{\sin \alpha - \cos \alpha }} = $
Let $0 < x < \frac{\pi }{4}.$ Then $\sec 2x - \tan 2x = $
If $2\sec 2\alpha = \tan \beta + \cot \beta ,$ then one of the values of $\alpha + \beta $ is
If $a\,\cos 2\theta + b\,\sin 2\theta = c$ has $\alpha$ and $\beta$ as its solution, then the value of $\tan \alpha + \tan \beta $ is