Question

prove euler's identities:

sin z =((e^iz)-(e^-iz))/2i

and

cos z = ((e^iz)+(e^-iz))/2

Answer 1

e^(iz)=cos(z)+isin(z) ...........1
e^(-iz)=cos(z)-isin(z) ..........2

subtract (2) from (1) you will get it.

Answer 2

by subtraction you will get sin z =((e^iz)-(e^-iz))/2i
and by addition of (1) and (2) you will have
cos z = ((e^iz)+(e^-iz))/2

Answer 3

thanks