The value of $\cos (270^\circ + \theta )\,\cos (90^\circ - \theta ) - \sin (270^\circ - \theta )\,\cos \theta $ is

The exact value of $\cos \frac{2\pi}{28} \csc \frac{3\pi}{28} + \cos \frac{6\pi}{28} \csc \frac{9\pi}{28} + \cos \frac{18\pi}{28} \csc \frac{27\pi}{28}$ is equal to

Maximum value of $5 \cos \theta + 3 \cos \left( \theta + \frac{\pi}{3} \right) - 1$ is

If $\sin \theta_1 + \sin \theta_2 + \sin \theta_3 = 3$,then $\cos \theta_1 + \cos \theta_2 + \cos \theta_3 = $

$A$ circular wire of diameter $10\,cm$ is cut and placed along the circumference of a circle of diameter $1\,m$. The angle subtended by the wire at the centre of the circle is equal to

If $\tan A = \frac{n}{n+1}$ and $\tan B = \frac{1}{2n+1}$,the value of $\tan (A+B) =$