Match Column I with Column II

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Match Column I with Column II.

Column I	Column II
(a) If $\alpha$ , $\beta$ , $\gamma$ , and $\delta$ are four solutions of $\tan\left(\theta+\frac{\pi}{4}\right)=3\tan3\theta$ , no two of which have equal tangents, then $\tan\alpha+\tan\beta+\tan\gamma+\tan\delta$ is	(p) $\sqrt{2}$
(b) If $\frac{\cos(\theta_1-\theta_2)}{\cos(\theta_1+\theta_2)}+\frac{\cos(\theta_3+\theta_4)}{\cos(\theta_3-\theta_4)}=0$ , then $\tan\theta_1\tan\theta_2\tan\theta_3\tan\theta_4$ is	(q) $\sqrt{3}$
(c) If $\sec(\alpha-\beta)$ , $\sec\alpha$ , and $\sec(\alpha+\beta)$ are in A.P., with $\beta\ne0$ , then $\cos\alpha\sec\frac{\beta}{2}$ is	(r) $-1$
(d) If $\cos\alpha=\frac{2\cos\beta-1}{2-\cos\beta}$ , where $0<\alpha<\beta<\pi$ , then $\frac{\tan\frac{\alpha}{2}}{\tan\frac{\beta}{2}}$ is	(s) $0$