The Curve $x = 5 - 10 \cos ^ { 2 } t , y = \tan t \left( 1 - 2 \cos ^ { 2 } t \right)$

question 45

Multiple Choice

The curve $x = 5 - 10 \cos ^ { 2 } t , y = \tan t \left( 1 - 2 \cos ^ { 2 } t \right)$ cross itself at some point $\left( x _ { 0 } , y _ { 0 } \right)$ . Find the equations of both tangent lines at that point.

• A) \(y = \frac { x } { 5 } , y = - \frac { x } { 10 }\)
• B)
• \(y = \frac { x } { 2 } - 10 , y = - \frac { x } { 2 } - 2\)
• C) \(y = x + 5 , y = - x + 5\)
• D)
• \(y = \frac { x } { 2 } , y = - \frac { x } { 2 }\)
• E)
• \(y = \frac { x } { 2 } + 8 , y = - \frac { x } { 2 } + 2\)

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