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9709 P31 - Jun 2017 - Q4
1621

The parametric equations of a curve are

\(x = \\ln \, \cos \theta\), \(y = 3\theta - \tan \theta\),

where \(0 \leq \theta < \frac{1}{2}\pi\).

(i) Express \(\frac{dy}{dx}\) in terms of \(\tan \theta\).

(ii) Find the exact \(y\)-coordinate of the point on the curve at which the gradient of the normal is equal to 1.

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