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AP EAMCET · Maths · Application of Derivatives

The sum of the lengths of the subtangent and the subnormal drawn at \(\theta=\frac{\pi}{3}\) on the cycloid \(x=a(\theta-\sin \theta)\) : \(y=a(1-\cos \theta)\) is

  1. A \(2 \sqrt{a}\)
  2. B \((2 \sqrt{3}) a\)
  3. C \(\frac{2 a}{\sqrt{3}}\)
  4. D \(\frac{a}{\sqrt{3}}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\frac{2 a}{\sqrt{3}}\)

Step-by-step Solution

Detailed explanation

Given \(\theta=\pi / 3\) and \(x=a(\theta-\sin \theta), y=a(1-\cos \theta)\) Differentiate it, w.r.t. ' \(\theta\) \[ \frac{d x}{d \theta}=a(1-\cos \theta), \frac{d y}{d \theta}=a(\sin \theta) \] Then,…