Method of Differentiation
Parametric Differentiation
JEE Main 2020
Grade 12
Question:
If $x = 2 \sin \theta - \sin 2\theta$ and $y = 2 \cos \theta - \cos 2\theta$, then $\frac{dy}{dx}$ at $\theta = \frac{\pi}{2}$ equals:
(1) $1$
(2) $-1$
(3) $\frac{1}{2}$
(4) $-\frac{1}{2}$
Step-by-Step Solution
Key Concept: Differentiate $x$ and $y$ separately with respect to $\theta$ and form $\frac{dy/d\theta}{dx/d\theta}$ — then substitute $\theta = \pi/2$ directly into that ratio.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)