10. Consider curve C defined by the following parametric equation: x=sin(t) y=sin(t) - sin (t) sin(t)...

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10. Consider curve C defined by the following parametric equation: x=sin(t) y=sin(t) - sin (t) sin(t) cos(t) 0 t < 2 (a) Show C has two tangent lines at the origin and find their equations. (b) At what value(s) of t does C have a vertical tangent? Bonus Question: Show that d sin (x) cos (x) + = = cos(2x) dx 1 + cot(x) 1 + tan(x) 10. Consider curve C defined by the following parametric equation: x=sin(t) y=sin(t) - sin (t) sin(t) cos(t) 0 t < 2 (a) Show C has two tangent lines at the origin and find their equations. (b) At what value(s) of t does C have a vertical tangent? Bonus Question: Show that d sin (x) cos (x) + = = cos(2x) dx 1 + cot(x) 1 + tan(x)