okay, so i was given the piecewise function f(t)= k if -pi/2< x< pi/2
0 if pi/2 < x < 3pi/2
i computed the series to be
which i think is right,
but now i need to show that
i know it is probably pretty simple but iam a bit stuck so what steps should i take to show this.
Yes, it's a common trick to evaluate infinite series using the fourier representation of a function and for a certain t. In this case we chose t=0 because it makes the cos term become 1 for all values of n. Another choice could have been 2pi, but then the LHS wouldn't be defined.