$Q$ is $14\, km$ south and $16\, km$ west of $P$. Find the distance of $Q$ from $P$ (in $km$).

$\sin 4\theta$ can be written as

If $\theta$ lies in the second quadrant,then the value of $\sqrt{\frac{1 - \sin \theta}{1 + \sin \theta}} + \sqrt{\frac{1 + \sin \theta}{1 - \sin \theta}}$ is:

If $A + B + C = 180^\circ,$ then $\frac{\sin 2A + \sin 2B + \sin 2C}{\cos A + \cos B + \cos C - 1} = $

$\log _{\frac{1}{8}\csc^2 \frac{\pi}{8}} \sin^2 \frac{3\pi}{8}$ equals to

Let ${f_k}(x) = \frac{1}{k}(\sin^k x + \cos^k x)$ for $k = 1, 2, 3, ...$. Then for all $x \in R$,the value of $f_4(x) - f_6(x)$ is equal to