Hi i need help with these 2 questions,
1) Prove that, if z=x+iy, then cotz = (sin2x-isinh2y)/(cos2y -cos2x)
i got,....cosz = cosxcoshy - isinxsinhy
and sinz = sinxcoshy + icosxsinhy
cotz = cosz/sinz
= (cosxcoshy - isinxsinhy) / sinxcoshy + icosxsinhy
Rationalizing and using double angle formula i get
cotz = (sin2x-isinh2y)/(cos2x-cosh2y)
2) By considering summation n=1 to N-1 of Z^2n and that Z=e^i@
show that summation n=1 to N-1 cos2nQ = (sinN@cos(N-1)@)/sin@,...sin@ not equal to zero
for the second one, i need an idea how to begin it....
P.S i wrote summation coz i dont know how to put that big E