If y=tan⁡θ+cot⁡θ,x=tan⁡θ−cot⁡θ, where θ is a parameter then y3d2ydx2 is equal to

y2−x2=4⇒2ydydx−2x=0⇒yd2ydx2+(dydx)2−1⇒yd2dx2+x2y2−1=0y3d2ydx2+x2−y2=0⇒y3d2ydx2=−x2+y2=4

If y=tan⁡θ+cot⁡θ,x=tan⁡θ−cot⁡θ, where θ is a parameter then y3d2ydx2 is equal to

y2−x2=4⇒2ydydx−2x=0⇒yd2ydx2+(dydx)2−1⇒yd2dx2+x2y2−1=0y3d2ydx2+x2−y2=0⇒y3d2ydx2=−x2+y2=4

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If $y = t a n θ + c o t θ, x = t a n θ - c o t θ,$ where $θ$ is a parameter then $y^{3} \frac{d^{2} y}{d x^{2}}$ is equal to

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$y^{2} - x^{2} = 4 \Rightarrow 2 y \frac{d y}{d x} - 2 x = 0$

$\Rightarrow y \frac{d^{2} y}{d x^{2}} + {(\frac{d y}{d x})}^{2} - 1 \Rightarrow y \frac{d^{2}}{d x^{2}} + \frac{x^{2}}{y^{2}} - 1 = 0$

$y^{3} \frac{d^{2} y}{d x^{2}} + x^{2} - y^{2} = 0 \Rightarrow y^{3} \frac{d^{2} y}{d x^{2}} = - x^{2} + y^{2} = 4$

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If y=tan⁡θ+cot⁡θ,x=tan⁡θ−cot⁡θ, where θ is a parameter then y3d2ydx2 is equal to

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If $y = t a n θ + c o t θ, x = t a n θ - c o t θ,$ where $θ$ is a parameter then $y^{3} \frac{d^{2} y}{d x^{2}}$ is equal to