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?

The roots of the equation 7x² - 6x + 1 = 0 are tan α and tan β, where 2α and 2β are the angles of a triangle. Which one of the following is correct?

What is the number of solutions of the equation cot2x cot3x = 1 for 0 < x