The Curve $x = 2 - 4 \cos ^ { 2 } t , \quad y = \tan t \left( 1 - 2 \cos ^ { 2 } t \right)$

Multiple Choice

The curve $x = 2 - 4 \cos ^ { 2 } t , \quad y = \tan t \left( 1 - 2 \cos ^ { 2 } t \right)$ cross itself at some point $\left( x _ { 0 } , y _ { 0 } \right)$ . Find the equations of both tangent lines at that point.

A) $y = \frac { x } { 2 } - 4 , y = - \frac { x } { 2 } - 2$
B) $y = \frac { x } { 2 } , y = - \frac { x } { 2 }$
C) $y = \frac { x } { 2 } , y = - \frac { x } { 4 }$
D) $y = \frac { x } { 2 } + 8 , y = - \frac { x } { 2 } + 2$
E) $y = x + 2 , y = - x + 2$