2015 17 From previous KVPY papers!

Geometry Level 4

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

Let f(x)f(x) denote the function above for constants A,B,C,DA,B,C,D and EE. Given that TT equals to

f(0)f(π5)+f(2π5)f(3π5)++f(8π5)f(9π5)\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 TT?

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