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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 22 of 50
Marks: +1, -0
If x=2cos⁡θ−cos⁡2θx=2\cos\theta-\cos 2\theta and y=2sin⁡θ−sin⁡2θy=2\sin\theta-\sin 2\theta, then   dydx\;\frac{dy}{dx} is
Solution:     👈: Video Solution
  Explanation: Given,     x=2cos⁡θ−cos⁡2θ\;\text{Explanation: Given, }\;\;x=2\cos\theta-\cos 2\theta
    and     y=2sin⁡θ−sin⁡2θ\;\;\text{and }\;\;y=2\sin\theta-\sin 2\theta
    Therefore,       dxdθ=−2sin⁡θ+2sin⁡2θ\;\;\text{Therefore, }\;\;\;\frac{dx}{d\theta}=-2\sin\theta+2\sin 2\theta
    and       dydθ=2cos⁡θ−2cos⁡2θ\;\;\text{and }\;\;\;\frac{dy}{d\theta}=2\cos\theta-2\cos 2\theta
∴    dydx=2cos⁡θ−2cos⁡2θ−2sin⁡θ+2sin⁡2θ\therefore\;\;\frac{dy}{dx}=\frac{2\cos\theta-2\cos 2\theta}{-2\sin\theta+2\sin 2\theta}
    or       dydx=cos⁡θ−cos⁡2θsin⁡2θ−sin⁡θ\;\;\text{or }\;\;\;\frac{dy}{dx}=\frac{\cos\theta-\cos 2\theta}{\sin 2\theta-\sin\theta}
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