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(A) Prove the orthogonality of the sine and cosine functions by showing the following: L m m (a) coS (27 n n L x), COS(27- COS(2TT L L -L L -x) cos(2n -x) dx = 0mn L m n m n (b) sin (27- L x), sin (27 20 ) = L sin(27 L x) dx = 0mn -L L x) sin (27 L m m n (c) cos(27 - ), sin(27 , x) ) COS(2TT L L -L L x) sin(27 , x) dx = 0 where omn denotes the Kronecker delta 1. m = n omn = 0, man