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?

$$ \text { What is } \frac{\sqrt{3} \cos 10^{\circ}-\sin 10^{\circ}}{\sin 25^{\circ} \cos 25^{\circ}} \text { equal to ? } $$