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

The value of $2({\sin ^6}\theta + {\cos ^6}\theta ) - 3({\sin ^4}\theta + {\cos ^4}\theta ) + 1$ is

Find the value of:

$\sin 75^{\circ}$

If $\tan \theta = \frac{{x\,\sin \,\phi }}{{1 - x\,\cos \,\phi }}$ and $\tan \,\phi = \frac{{y\sin \,\theta }}{{1 - y\,\cos \,\theta }}$, then $\frac{x}{y} = $

Prove the $\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right]=1$

If $\sec \theta + \tan \theta = p,$ then $\tan \theta $ is equal to