The value of $2({\sin ^6}\theta + {\cos ^6}\theta ) - 3({\sin ^4}\theta + {\cos ^4}\theta ) + 1$ is
$2$
$0$
$4$
$6$
$tan\,\, 20^o + tan\,\, 40^o + \sqrt 3\,\, tan\,\, 20^o tan\,\, 40^o$ is equal to
The value of $k$, for which ${(\cos x + \sin x)^2} + k\,\sin x\cos x - 1 = 0$ is an identity, is
If $\sin x + {\sin ^2}x = 1$, then the value of ${\cos ^{12}}x + 3{\cos ^{10}}x + 3{\cos ^8}x + {\cos ^6}x - 2$ is equal to
$\cot x - \tan x = $
Find the value of the trigonometric function $\tan \frac{19 \pi}{3}$.