Method of Differentiation
Parametric Differentiation
IIT-JEE 1999
Grade 12
Question:
If $x = a(\theta - \sin \theta)$ and $y = a(1 - \cos \theta)$, then the value of $\frac{d^2y}{dx^2}$ at $\theta = \frac{\pi}{2}$ is:
(1) $-\frac{1}{a}$
(2) $\frac{1}{a}$
(3) $-\frac{1}{4a}$
(4) $\frac{1}{4a}$
Step-by-Step Solution
Key Concept: First find $\frac{dy}{dx} = \frac{dy/d\theta}{dx/d\theta}$ and simplify it to $\cot(\theta/2)$ before differentiating again with respect to $\theta$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)