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