At what time between $10\,\,O'clock$ and $11\,\,O 'clock$ are the two hands of a clock symmetric with respect to the vertical line (give the answer to the nearest second)?
$10h\,9m \,13s$
$10h \,9m \,14s$
$10h \,9m \,22s$
$10h \,9m \,50s$
If the arcs of the same lengths in two circles subtend angles $65^{\circ}$ and $110^{\circ}$ at the centre, find the ratio of their radii.
Find the value of the trigonometric function $\sin 765^{\circ}$
If $\cot x=-\frac{5}{12}, x$ lies in second quadrant, find the values of other five trigonometric functions.
If $A + B + C = \pi $ and $\cos A = \cos B\,\cos C,$ then $\tan B\,\,\tan C$ is equal to
If $\tan A + \cot A = 4,$ then ${\tan ^4}A + {\cot ^4}A$ is equal to