The value of the expression $(sinx + cosecx)^2 + (cosx + secx)^2 - ( tanx + cotx)^2$ wherever defined is equal to

Prove that: $\frac{\sin 5 x+\sin 3 x}{\cos 5 x+\cos 3 x}=\tan 4 x$

If $A = 580^o$ then which one of the following is true

If $sin t + cos t = \frac{1}{5}$ then $tan \frac{t}{2}$ is equal to :

$\left( {\frac{{\sin 2A}}{{1 + \cos 2A}}} \right)\,\left( {\frac{{\cos A}}{{1 + \cos A}}} \right)= $

The value of $\sin \frac{\pi }{{14}}\sin \frac{{3\pi }}{{14}}\sin \frac{{5\pi }}{{14}}\sin \frac{{7\pi }}{{14}}\sin \frac{{9\pi }}{{14}}\sin \frac{{11\pi }}{{14}}\sin \frac{{13\pi }}{{14}}$ is equal to