In class we used the fact that sine functions are orthogonal in order to find the amplitudes of the normal modes of a plucked string. In this question we will prove it. L (a) Prove that: for sin (nxx/L) sin (mTx/L)dr == L Sn,m 2 L L (b) Prove that: for cos(nÃx/L) cos(mä/L)dx = dn,m 2 Remember the Krönecker delta 8n,m is defined as бn,m = 1 if n = m and 8n,m = 0 if n + m. Hint: you may want to do the integrals for n = m and nm separately.