Given that
$$y = \tan x$$
use the quotient rule to show that
$$\frac { \mathrm { d } y } { \mathrm {~d} x } = \sec ^ { 2 } x$$
10
The region enclosed by the curve \(y = \tan ^ { 2 } x\) and the horizontal line, which intersects the curve at \(x = - \frac { \pi } { 4 }\) and \(x = \frac { \pi } { 4 }\), is shaded in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{042e248a-9efa-4844-957d-f05715900ffc-17_1059_967_461_539}
Show that the area of the shaded region is
$$\pi - 2$$
Fully justify your answer.
Do not write outside the box
\includegraphics[max width=\textwidth, alt={}, center]{042e248a-9efa-4844-957d-f05715900ffc-19_2488_1716_219_153}