25 (i) A function f satisfies the two conditions f(-t) = f(t) and f(t + ;) = -f(t) for all t. Show that its Fourier coefficients satisfy do = a2 = Q4 = 06 = . . . = 0, b1 = b2 = b3 = b4 = . . . = 0. (ii) A function f satisfies the two conditions f(-t) = -f(t) and f(t + ;) = -f(t) for all t. Show that its Fourier coefficients satisfy do = a1 = a2 = a3 = . . . = 0, b2 = b4 = b6 = . . . = 0. (i ) Hint : fit) = Got I ap . coszickx + I bk. SinaTik x. 1= 1 k=1 do = 1 2 fitiat . ak = J : fits cossacktat bK = J + fits sinzTiktat fl - t ) = fit) 7 fits is an even function ?) Go= 0, bi = 62 = by = by= = 0 use f (t+ 2) = - fit) to show ak= D if k is even. (ii ) Similar