The potential energy in joules of an oscillating spring can be represented by the expression [math]16k[\frac{\csc^2(2\pi t)-1}{\csc^2(2\pi t)}][/math], where [math]k[/math] is a constant and [math]t[/math] is the time in seconds since the spring began oscillating. Create a two-column proof to show that the potential energy of the spring can also be written as [math]16k \cos^2 (2\pi t)[/math].
