In class, you were given the following expression for electromagnetic torque for a two-pole round-\ rotor synchronous machine:\ Te = 3\ 2 LAi\ f d\ [\ (ias 0.5ibs 0.5ics) cos \\\\theta r + 3/2(ibs ics) sin \\\\theta r\ ]\ . (1)\ By assuming that ias, ibs, ics constitute a balance set of sinusoidal waveforms [e.g, ias(t) = 2I cos(\\\\omega et \\\\pi /2), ibs(t) =2I cos(\\\\omega et2\\\\pi /3\\\\pi /2), and ics(t) = 2I cos(\\\\omega et+2\\\\pi /3\\\\pi /2)]; i\ f d(t) is constant because it is a dc quatity in quasi-steady\ state, and \\\\theta r (t) = \\\\omega et + \\\\delta (for constant electrical angular speed \\\\omega e and fixed angle \\\\delta ), prove that the electromagnetic torque\ Te(t) is constant for any fixed \\\\delta . Hint: Use trigonometric identities of product to addition of sinusoidal functions.