If $f_n(x) = \frac{1}{2n} [\sin^{2n} x + \cos^{2n} x]$,then $f_1(x) + f_2(x) - f_3(x) =$

If $a = \sin \frac{\pi}{18} \sin \frac{5\pi}{18} \sin \frac{7\pi}{18}$ and $x$ is the solution of the equations $y = 2[x] + 2$ and $y = 3[x - 2]$,where $[x]$ denotes the greatest integer function of $x$,then $a$ is equal to:

If $\sin \alpha = \sin \beta$ and $\cos \alpha = \cos \beta$,then $\alpha - \beta = $ for some integer $n$.

$\frac{\tan A + \sec A - 1}{\tan A - \sec A + 1} = $

If angle $\theta$ is divided into two parts such that the tangent of one part is $k$ times the tangent of the other and $\phi$ is their difference,then $\sin \theta = $

In a $\Delta ABC$,if the median,bisector,and altitude drawn from the vertex $A$ divide the angle at the vertex into four equal parts,then the angles of the $\Delta ABC$ are: