Which of the following is correct?

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

If $\sin \theta = \frac{3}{5},$ then the value of $\frac{\tan \theta + \cos \theta}{\cot \theta + \operatorname{cosec} \theta}$ is equal to

$A$ telegraph post is bent at a point above the ground due to a storm. Its top just touches the ground at a distance of $10 \sqrt{3} \text{ m}$ from its foot and makes an angle of $30^{\circ}$ with the horizontal. Then,the height (in meters) of the telegraph post is:

$\tan \left( \frac{\pi }{4} + \theta \right) - \tan \left( \frac{\pi }{4} - \theta \right) = $

If $\cos \theta = -\frac{\sqrt{3}}{2}$ and $\sin \alpha = -\frac{3}{5}$,where $\theta$ does not lie in the third quadrant and $\alpha$ lies in the third quadrant,find the value of $\frac{2 \tan \alpha + \sqrt{3} \tan \theta}{\cot^2 \theta + \cos \alpha}$.