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NDA 2021 Maths · Mathematics · Derivatives · medium

If x=3cos θ and y=3sin θ, then dy/dx at θ=(π)/(4) is

Single correct option

If x=3cos⁡θx=3\cos\theta and y=3sin⁡θy=3\sin\theta, then dydx\dfrac{dy}{dx} at θ=π4\theta=\dfrac\pi4 is
  1. A. 11
  2. B. −3-3
  3. C. 00
  4. D. −1-1
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Answer: (D) −1-1

dydx=3cos⁡θ−3sin⁡θ=−cot⁡θ=−1\dfrac{dy}{dx}=\dfrac{3\cos\theta}{-3\sin\theta}=-\cot\theta=-1 at θ=π/4\theta=\pi/4. It is the slope of the tangent to the circle x2+y2=9x^2+y^2=9 at (32,32)\left(\tfrac3{\sqrt2},\tfrac3{\sqrt2}\right), which must be negative.
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Original question written in the NDA 2021 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