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If x = cos t(3 - 2cos2t) and y = sin t (3 - 2sin2t), then find the value of \(\frac{dy}{dx}\) at t = \(\frac{\pi}{4}\).

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Given,

x = cos t(3 - 2cos2t)

Differentiating both sides with respect to t, we get

Differentiating both sides with respect to t, we get

∴ \(\frac{dy}{dx}]_{t=\frac{\pi}{4}}\)

\(= cot\,\frac{\pi}{4}=1\)

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