If ${\rm{cosec }}A + \cot A = \frac{{11}}{2},$ then $\tan A = $

If $\sin x = \frac{{ - 24}}{{25}},$ then the value of $\tan \, x$ is

If $\sin \theta = - \frac{1}{{\sqrt 2 }}$ and $\tan \theta = 1,$ then $\theta $ lies in which quadrant

Find the values of other five trigonometric functions if $\sec x=\frac{13}{5}, x$ lies in fourth quadrant.

If $5\tan \theta = 4,$ then $\frac{{5\sin \theta - 3\cos \theta }}{{5\sin \theta + 2\cos \theta }} = $

Let $A, B$ and $C$ are the angles of a plain triangle and $\tan \frac{A}{2} = \frac{1}{3},\,\,\tan \frac{B}{2} = \frac{2}{3}$. Then $\tan \frac{C}{2}$ is equal to