If $$\sin \theta + \cos \theta = \sqrt 2 \cos \theta $$, then what is $$(\cos \theta - \sin \theta )$$ equal to?

If $$\sin \theta = - {1 \over 2}$$ and $$\tan \theta = {1 \over {\sqrt 3 }}$$, then in which quadrant does $$\theta$$ lie?

If $$p = \cos ec\theta - \cot \theta $$ and $$q = {(\cos ec\theta + \cot \theta )^{ - 1}}$$, then which one of the following is correct?

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?