Answer :

x = e^{cos2t} and y = e^{sin2t}

Now x = e^{cos2t},

Taking log on both sides to get,

log x = cos 2t

For y = e^{sin2t}

Taking log on both sides we get,

log y = sin 2t

∴ cos^{2}2t + sin^{2}2t = (log x)^{2} + (log y)^{2}

1 = (log x)^{2} + (log y)^{2}

Differentiating w.r.t x,

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