If $\frac{{3\pi }}{4} < \alpha < \pi ,$ then $\sqrt {{\rm{cose}}{{\rm{c}}^2}\alpha + 2\cot \alpha } $ is equal to
$1 + \cot \alpha $
$1 - \cot \alpha $
$ - 1 - \cot \alpha $
$ - 1 + \cot \alpha $
If $\sin x + {\rm{cosec}}\,x = 2,$ then $sin^n x + cosec^n x$ is equal to
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.
The equation ${\sec ^2}\theta = \frac{{4xy}}{{{{(x + y)}^2}}}$ is only possible when
The circular wire of diameter $10\,cm$ is cut and placed along the circumference of a circle of diameter $1\, metre.$ The angle subtended by the wire at the centre of the circle is equal to
Prove that $\sin (n+1) x \sin (n+2) x+\cos (n+1) x \cos (n+2) x=\cos x$