\text { Given that } x=e^{t} \cos t \text { and } y=e^{t} \sin t \text {, show that } \left(\frac{d x}{d t}\right)^{2}+\left(\frac{d y}{d t}\right)^{2}=2 e^{2 t} \frac{d y}{d x}=\frac{\tan t+1}{1-\tan t}

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