Mathematics

Problem

Match the statement of Column I with values of Column II.

Column I	Column II
(A) The number of solutions of the equation $\cot x = \cot x + \frac{1}{\sin x}$ ( $0 < x < \pi$ ) is	(p) no solution
(B) If $\sin \theta + \sin \phi = \frac{1}{2}$ and $\cos \theta + \cos \phi = 2$ , then value of $\cot \left(\frac{\theta + \phi}{2}\right)$ is	(q) $\frac{1}{3}$
(C) The value of $\sin^2 \alpha + \sin \left(\frac{\pi}{3} - \alpha\right) \sin \left(\frac{\pi}{3} + \alpha\right)$ is	(r) 1
(D) If $\tan \theta = 3 \tan \phi$ , then maximum value of $\tan^2(\theta - \phi)$ is	(s) 2
	(t) 4