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Assisting FullSimplify

I started with the expression e1 below. FullSimplify does not make any
progress in making it simpler. By a mixture of working on parts of the
expression, luck and physical reasoning I worked out that the expression is
the same as that given in e2. (For example I knew the expression should be
real). Is there anyway that I could have directed FullSimplify to get from
e1 to e2, by for example setting options?

(Cutting and pasting the code below into a notebook will make it readable.
It may then be evaluated.)


Hugh Goyder

e1 = (4*I*
E^(I*(a + b)*k)*(-E^(2*I*a*k) +
E^(2*I*(1 + ar)*k)))/(E^(2*I*(1 + a + ar)*k)*(-2 + Sr) +
E^(2*I*(a + b)*k)*(-2 + Sr) - E^(4*I*a*k)*Sr + E^(2*I*(1 + ar)*k)*Sr +
E^(2*I*(2*a + b)*k)*Sr - E^(2*I*(1 + ar + b)*k)*Sr -
E^(2*I*a*k)*(2 + Sr) - E^(2*I*(1 + a + ar + b)*k)*(2 + Sr))

e2 = -(Sin[(1 - a + ar)*k]/((-Cos[(1 + ar)*k])*Cos[b*k] +
Sr*Cos[a*k]*Sin[(1 - a + ar)*k]*Sin[b*k]))


FullSimplify[e1 == e2]



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