The value of $\sum_{r=1}^{18} \cos^2(5r)^\circ$,where $x^\circ$ denotes the $x$ degree,is equal to

Let the set of all $a \in \mathbb{R}$ such that the equation $\cos 2x + a \sin x = 2a - 7$ has a solution be $[p, q]$ and $r = \tan 9^{\circ} - \tan 27^{\circ} - \frac{1}{\cot 63^{\circ}} + \tan 81^{\circ}$,then $pqr$ is equal to ....................

If $\sin x + \sin^2 x = 1$,then the value of the expression $\cos^{12} x + 3\cos^{10} x + 3\cos^8 x + \cos^6 x - 1$ is equal to

If $\sin \alpha = \sin \beta$ and $\cos \alpha = \cos \beta$,then $\alpha - \beta = $ for some integer $n$.

Let $E = \left( 1 - \frac{\cos 61^\circ}{\cos 1^\circ} \right) \left( 1 - \frac{\cos 62^\circ}{\cos 2^\circ} \right) \dots \left( 1 - \frac{\cos 119^\circ}{\cos 59^\circ} \right)$,then $E$ is equal to:

If $\sin \theta \cosh \alpha = \tan x$ and $\cos \theta \sinh \alpha = \sec x$,then find the value of $\cos 2 \theta \cosh 2 \alpha$.