# Surface Area of Parametric Equation

Calculus Level 3

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

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

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

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