If $sin\theta_1 + sin\theta_2 + sin\theta_3 = 3,$ then $cos\theta_1 + cos\theta_2 + cos\theta_3=$
$3$
$2$
$1$
$0$
If $\sin \theta + \cos \theta = m$ and $\sec \theta + {\rm{cosec}}\theta = n$, then $n(m + 1)(m - 1) = $
If $\sin x + {\sin ^2}x = 1,$ then ${\cos ^8}x + 2{\cos ^6}x + {\cos ^4}x = $
If $\tan \theta = - \frac{1}{{\sqrt {10} }}$ and $\theta $ lies in the fourth quadrant, then $\cos \theta = $
Find the value of the trigonometric function $\tan \frac{19 \pi}{3}$.
The angle subtended at the centre of a circle of radius $3$ metres by an arc of length $1$ metre is equal to