If $0 < x < \pi $ and $\cos x + \sin x = \frac{1}{2}$,then $tan \,x$ is
$\frac{{1 - \sqrt 7 }}{4}$
$\;\frac{{4 - \sqrt 7 }}{3}$
$ - \frac{{4 + \sqrt 7 }}{3}$
$\;\frac{{1 + \sqrt 7 }}{4}$
If $\sin x = \frac{{ - 24}}{{25}},$ then the value of $\tan \, x$ is
If in two circles, arcs of the same length subtend angles $60^{\circ}$ and $75^{\circ}$ at the centre, find the ratio of their radii.
If $A$ lies in the second quadrant and $3\tan A + 4 = 0,$ the value of $2\cot A - 5\cos A + \sin A$ is equal to
The value of ${\sin ^2}{5^o} + {\sin ^2}{10^o} + {\sin ^2}{15^o} + ... + $ ${\sin ^2}{85^o} + {\sin ^2}{90^o}$ is equal to
If $\cos x=-\frac{3}{5}, x$ lies in the third quadrant, find the values of other five trigonometric functions.