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

What is the general solution of cos¹⁰⁰ x - sin¹⁰⁰ x = 1?