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NDA 2018 Maths · Mathematics · Derivatives · medium

If x=2cos t and y=2sin t, then dy/dx at t=(π)/(6) is

Single correct option

If x=2cos⁡tx=2\cos t and y=2sin⁡ty=2\sin t, then dydx\frac{dy}{dx} at t=π6t=\frac\pi6 is
  1. A. 3\sqrt3
  2. B. −13-\frac1{\sqrt3}
  3. C. 13\frac1{\sqrt3}
  4. D. −3-\sqrt3
Show answer and solution

Answer: (D) −3-\sqrt3

dydx=dy/dtdx/dt=2cos⁡t−2sin⁡t=−cot⁡t\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{2\cos t}{-2\sin t}=-\cot t. At t=π6t=\frac\pi6, cot⁡t=3\cot t=\sqrt3, so the slope is −3-\sqrt3. The value −13-\frac1{\sqrt3} uses tan⁡t\tan t in place of cot⁡t\cot t.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake