1.8.5 Example E Show that cos(ak – a/2) 2 sin(a/2) E sin(ak) (1.269) Taking the difference of cos(ak), A cos(ak) = -2 sin(a/2) sin(ak + a/2), (1.270) and replacing k by k – 1/2 gives A cos(ak – a/2) =...

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Extracted text: 1.8.5 Example E Show that cos(ak – a/2) 2 sin(a/2) E sin(ak) (1.269) Taking the difference of cos(ak), A cos(ak) = -2 sin(a/2) sin(ak + a/2), (1.270) and replacing k by k – 1/2 gives A cos(ak – a/2) = -2 sin(a/2) sin(ak). (1.271) Now dividing by -2 sin(a/2) and applying the operator A-1 gives cos(ak – a/2) 2 sin(a/2) A-1 sin(ak) : (1.272) which, up to a constant, is equation (1.269).