$1 - 2{\sin ^2}\left( {\frac{\pi }{4} + \theta } \right) = $

The value of $\cos(18^{\circ}-A) \cos(18^{\circ}+A) - \cos(72^{\circ}-A) \cos(72^{\circ}+A)$ is equal to

If $\sin x + \sin y = \frac{1}{2}$ and $\cos x + \cos y = 1$,then $\tan(x + y) = $

Find the value of: $\tan 15^{\circ}$

In an isosceles right-angled triangle,a straight line is drawn from the midpoint of one of the equal sides to the opposite vertex. Then a pair of possible values of the cotangents of the two angles so formed at that vertex are

$\cos 48^{\circ} \cdot \cos 12^{\circ} = ?$