First find point of contact!

Calculus Level 5

A curve is parametrically represented as

{x=cost+ln(tant2)y=sint,\begin{cases} x = \cos t+\ln \left(\tan\frac{t}{2}\right) \\ y = \sin t, \end{cases}

where tt is a parameter.

Find the length of tangent to the curve at the point where its xx-coordinate is equal to its yy-coordinate.

The length of tangent is defined as the distance between the point of contact with the curve and the point where the tangent meets the xx-axis.

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