Surface Area of Parametric Equation

Calculus Level 4

P:={y=tantx=sect\mathcal{P} := \begin{cases} y= \tan t \\ x = \sec t \end{cases}

The curve P \mathcal{P} is defined using the above pair of parametric equations for all real values of t t such that cost0 \cos t \neq 0.

What is the surface area of the solid of revolution obtained by revolving P \mathcal{P} about x x-axis for 0<t<π40 < t < \frac{\pi}{4} ?

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