Question #5b420

1 Answer
P dilip_k
Feb 3, 2018

By Euler's formula we can write

#cos(alpha+beta) +isin(alpha+beta)=e^(i(alpha+beta)#

#=>cos(alpha+beta) +isin(alpha+beta)=e^(ialpha)*e^(ibeta)#

#=>cos(alpha+beta) +isin(alpha+beta)=(cosalpha+isinalpha)(cosbeta+isinbeta)#
#=(cosalphacosbeta-sinalphasinbeta)+i(sinalphacosbeta+cosalphasinbeta)#

Equating imaginary part on both sides we get

#sin(alpha+beta)=sinalphacosbeta+cosalphasinbeta#

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