If $x\, sin \theta = y\, sin \, \left( {\theta \,\, + \,\,\frac{{2\,\pi }}{3}} \right) = z\, sin \, \left( {\theta \,\, + \,\,\frac{{4\,\pi }}{3}} \right)$ then :
$x + y + z = 0$
$xy + yz + zx = 0$
$xyz + x + y + z = 1$
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$\frac{{\cos A}}{{1 - \sin A}} = $
If $\tan A = \frac{{1 - \cos B}}{{\sin B}},$ find $\tan 2A$ in terms of $\tan B$ and show that
In the figure, $\theta_1+\theta_2=\frac{\pi}{2}$ and $\sqrt{3}(B E)=4(A B)$. If the area of $\triangle CAB$ is $2 \sqrt{3}-3$ unit $^2$, when $\frac{\theta_2}{\theta_1}$ is the largest, then the perimeter (in unit) of $\triangle CED$ is equal to $...........$.
$\cos 2(\theta + \phi ) - 4\cos (\theta + \phi )\sin \theta \sin \phi + 2{\sin ^2}\phi = $
$1 - 2{\sin ^2}\left( {\frac{\pi }{4} + \theta } \right) = $