The value of $\cos ^{2} 45^{\circ}-\sin ^{2} 15^{\circ}$ is

Find the value of: $\sin 75^{\circ}$

$(\cos \alpha + \cos \beta )^2 + (\sin \alpha + \sin \beta )^2 = $

Prove that $\frac{\cos 9x - \cos 5x}{\sin 17x - \sin 3x} = -\frac{\sin 2x}{\cos 10x}$

If $\theta+\phi=\frac{\pi}{4}$, then $(1+\tan \theta)(1+\tan \phi)$ is equal to

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