2015 17 From previous KVPY papers!

Geometry Level 4

\( f(x) = \cos(5x) + A\cos(4x) + B\cos(3x) + C\cos(2x) + D\cos(x) + E\)

Let \(f(x) \) denote the function above for constants \(A,B,C,D\) and \(E\). Given that \(T\) equals to

\(\large f\left( 0 \right) -f\left( \frac { \pi }{ 5 } \right) +f\left( \frac { 2\pi }{ 5 } \right) -f\left( \frac { 3\pi }{ 5 } \right) + \cdots+f\left( \frac { 8\pi }{ 5 } \right) -f\left( \frac { 9\pi }{ 5 } \right) \)

Which of the following answer choices shows the property of \(T\)?

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