In a triangle $\tan A + \tan B + \tan C = 6$ and $\tan A\tan B = 2,$ then the values of $\tan A,\,\,\tan B$ and $\tan C$ are
$1, 2, 3$
$2,1,3$
$(a)$ and $(b)$ both
None of these
$\sin 4\theta $ can be written as
If $\cos x + \cos y + \cos \alpha = 0$ and $\sin x + \sin y + \sin \alpha = 0,$ then $\cot \,\left( {\frac{{x + y}}{2}} \right) = $
$\cos A + \cos (240^\circ + A) + \cos (240^\circ - A) = $
${\cos ^2}A{(3 - 4{\cos ^2}A)^2} + {\sin ^2}A{(3 - 4{\sin ^2}A)^2} = $
If $\sin \theta+\cos \theta=\frac{1}{2}$, then $16(\sin (2 \theta)+\cos (4 \theta)+\sin (6 \theta))$ is equal to: