If $x+\frac{1}{x}=2\cos \theta$ then what is $x^{3}+\frac{1}{x^{3}}$ equal to?

If $0\le x\le \frac{\pi }{2}$ then what is the number of values of x satisfying the equation $\tan x+\sec x=2\cos x$

Consider the following for the three (03) items that follow: Let $p=\sin 35{}^{\circ }$, $q=\sin 25{}^{\circ }$ and $r=\sin (-95{}^{\circ })$. 

What is $(p+q+r)$ equal to?

Consider the following for the three (03) items that follow: Let $p=\sin 35{}^{\circ }$, $q=\sin 25{}^{\circ }$ and $r=\sin (-95{}^{\circ })$. 

What is $(pq+qr+rp)$ equal to?