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

$\frac{\sin^3 \theta - \cos^3 \theta}{\sin \theta - \cos \theta} - \frac{\cos \theta}{\sqrt{1 + \cot^2 \theta}} - 2 \tan \theta \cot \theta = -1$ if

The length of an arc which subtends an angle $18^{\circ}$ at the centre of the circle of radius $6 \text{ cm}$ is (in $\text{cm}$)

If $x \sin 45^{\circ} = y \operatorname{cosec} 30^{\circ}$,then $\frac{x^{4}}{y^{4}}$ is equal to (in $^{3}$)

If $\cos (\theta - \alpha ), \cos \theta$ and $\cos (\theta + \alpha )$ are in $H.P.$,then $\cos \theta \sec \frac{\alpha }{2}$ is equal to

From two points,lying on the same horizontal line,the angles of elevation of the top of the pillar are $\theta$ and $\phi$ $(\theta < \phi)$. If the height of the pillar is $h$ $m$ and the two points lie on the same side of the pillar,then the distance between the two points is (in $m$):