Question #60173

1 Answer
P dilip_k
Nov 30, 2017

By Eular's formula we have

#cosz+isinz=e^(iz).......[1]#

#cosz-isinz=e^(-iz).......[2]#

Adding [1] and [2] we get

#cosz=(e^(iz)+e^(-iz))/2#

#=>cos^2z=[(e^(iz)+e^(-iz))/2]^2#

#=>cos^2z=1/4(e^(iz)+e^(-iz))^2#

#=>2cos^2z=1/2(e^(2iz)+e^(-2iz)+2*e^(iz)*e^(-iz))#

#=>2cos^2z=(e^(2iz)+e^(-2iz))/2+1#

#=>2cos^2z=cos2z+1#

#=>cos2z+1=2cos^2z#

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