If $\tan \beta = \cos \theta \tan \alpha ,$ then ${\tan ^2}\frac{\theta }{2} = $
$\frac{{\sin (\alpha + \beta )}}{{\sin (\alpha - \beta )}}$
$\frac{{\cos (\alpha - \beta )}}{{\cos (\alpha + \beta )}}$
$\frac{{\sin (\alpha - \beta )}}{{\sin (\alpha + \beta )}}$
$\frac{{\cos (\alpha + \beta )}}{{\cos (\alpha - \beta )}}$
If $x + y = 3 - cos4\theta$ and $x - y = 4 \,sin2\theta$ then
Prove that $\cos ^{2} 2 x-\cos ^{2} 6 x=\sin 4 x \sin 8 x$
$\cos A + \cos (240^\circ + A) + \cos (240^\circ - A) = $
If $x\, sin \theta = y\, sin \, \left( {\theta \,\, + \,\,\frac{{2\,\pi }}{3}} \right) = z\, sin \, \left( {\theta \,\, + \,\,\frac{{4\,\pi }}{3}} \right)$ then :
If $sin t + cos t = \frac{1}{5}$ then $tan \frac{t}{2}$ is equal to :