$\sin \frac{\pi }{{14}}\sin \frac{{3\pi }}{{14}}\sin \frac{{5\pi }}{{14}}\sin \frac{{7\pi }}{{14}}\sin \frac{{9\pi }}{{14}}\sin \frac{{11\pi }}{{14}}\sin \frac{{13\pi }}{{14}}$ का मान होगा

$\frac{{\cos A}}{{1 - \sin A}} = $

यदि $\tan x = \frac{{2b}}{{a - c}}(a \ne c),$

$y = a\,{\cos ^2}x + 2b\,\sin x\cos x + c\,{\sin ^2}x$

तथा  $z = a{\sin ^2}x - 2b\sin x\cos x + c{\cos ^2}x,$ हो, तब

$2 \sin \left(\frac{\pi}{8}\right) \sin \left(\frac{2 \pi}{8}\right) \sin \left(\frac{3 \pi}{8}\right) \sin \left(\frac{5 \pi}{8}\right) \sin \left(\frac{6 \pi}{8}\right) \sin \left(\frac{7 \pi}{8}\right)$ का मान है -

यदि $\sin 6\theta = 32{\cos ^5}\theta \sin \theta - 32{\cos ^3}\theta \sin \theta + 3x,$ तब  $x = $

$\frac{{\sec 8A - 1}}{{\sec 4A - 1}} = $