Q. The function $f(\theta) = \frac{d}{d\theta}\int_{0}^{\theta}\frac{dx}{1 - \cos{\theta\cos x}}$ satisfies the differential equation
A) $\frac{df}{d\theta} + 2f(\theta) = 0$
B) $\frac{df}{d\theta} - 2f(\theta) = 0$
C) $\frac{df}{d\theta} - 2f(\theta) = \tan\theta$
D) $\frac{df}{d\theta} + 2f(\theta)\cot\theta = 0$
Explanation
The correct answer is Option D: $\frac{df}{d\theta} + 2f(\theta)\cot\theta = 0$.
A detailed explanation for this question is being prepared.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.