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
$\frac{\pi }{4} \,\,radian$
$\frac{\pi }{3}radian$
$\frac{\pi }{5}\,\,radian$
$\frac{\pi }{{10}}\,\,radian$
If $\sin x + {\sin ^2}x = 1$, then the value of ${\cos ^{12}}x + 3{\cos ^{10}}x + 3{\cos ^8}x + {\cos ^6}x - 2$ is equal to
If $\sin (\alpha - \beta ) = \frac{1}{2}$ and $\cos (\alpha + \beta ) = \frac{1}{2},$ where $\alpha $ and $\beta $ are positive acute angles, then
If the arcs of the same length in two circles $S_1$ and $S_2$ subtend angles $75^o $ and $120^o $ respectively at the centre. The ratio $\frac{{{S_1}}}{{{S_2}}}$ is equal to
If $\tan \theta = - \frac{1}{{\sqrt {10} }}$ and $\theta $ lies in the fourth quadrant, then $\cos \theta = $
Prove the $\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right]=1$