Q. The value of $\frac{\cot^{2}{\theta + 1}}{\cot^{2}{\theta - 1}}$ is equal to
A) $\sin{2\theta}$
B) $\cos{2\theta}$
C) $cosec\ 2\theta$
D) $\sec{2\theta}$
Explanation
(d)
$\frac{\cot^{2}{\theta + 1}}{\cot^{2}{\theta - 1}} = \frac{1 + \tan^{2}\theta}{1 - \tan^{2}\theta} = \frac{1}{\cos^{2}{\theta - \sin^{2}\theta}}$
$= \frac{1}{\cos{2\theta}} = \sec{2\theta}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.