First find point of contact!

Calculus Level 5

A curve is parametrically represented as \[\begin{cases} x = \cos t+\ln \left(\tan \left(\dfrac{t}{2}\right)\right) \\ y = \sin t \end{cases} \] where \(t\) is a parameter.

Find the length of tangent to the curve at the point where its \(x\) coordinate is equal to \(y\) coordinate.

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

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