Method of Differentiation
Parametric Differentiation
Premium Question
Grade 12
Question:
If $x = \sec \theta - \cos \theta$ and $y = \sec^n \theta - \cos^n \theta$, then $(x^2 + 4) \left(\frac{dy}{dx}\right)^2$ equals:
(1) $n^2(y^2 + 4)$
(2) $n^2(y^2 - 4)$
(3) $n^2(x^2 + 4)$
(4) $n^2y^2$
Step-by-Step Solution
Key Concept: First show that $x^2 + 4 = (\sec \theta + \cos \theta)^2$ and $y^2 + 4 = (\sec^n \theta + \cos^n \theta)^2$, then form $\frac{dy/d\theta}{dx/d\theta}$ and compare squares.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)