Let us assume

We know that

If f(2a – x) = f(x)

than

since sin2π – x = – sinx and cos2π – x = cosx and (–sinx)¹⁰⁰ = sin¹⁰⁰x ……equation 1

By property, we know that

……equation 2 since cosπ – x = cosx

Adding equation 1 and equation 2

We know

thus

2I = 0

I = 0