See attachment

\fa We know that, a set of sequence of functions ffor, for - -- Low -- f (x )- } is said to be orthogonal over an interval ( a, b) with respect to a weight function Roy zo if for all integer values of n and in with n Im the inner product of f with of Satisfies Here the inner product is zero for all Combinations of m and n values with m # n . Now, given function is $ ( 1) = Sin ( n - 1) x and interval is [o, 71 ] Here we take row - 1 .() we calculate the inner products. sin / m - 1 ) x , Sim ( n - t ) x ) [ " Sm / m - 1 ) x . Sim / n -+ )or An\f