Answer
The equation of the tangent is $y=2x+\frac{2-\pi}{2}$
Work Step by Step
$f'(x)=\dfrac{d}{dx}\tan{x}=\sec^2{x}$.
$f'(\frac{\pi}{4})=\sec^2{\frac{\pi}{4}}=2$.
Equation of tangent:
$(y-y_0)=m(x-x_0)$ at point $(x_0, y_0)$ and slope $m$.
$(y-1)=2(x-\frac{\pi}{4})\rightarrow y=2x+\frac{2-\pi}{2}$.
A graphing calculator and a computer algebra system have been used to confirm these results.
