How do you use the sum to product formulas to write the sum or difference #sin(alpha+beta)-sin(alpha-beta)# as a product?

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Answer 1 · 2017-01-13T13:51:42

The answer is #=2cosalphasinbeta#

#sin(A+-B)=sinAcosB+-cosAsinB#

Therefore

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

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

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

#=cancel(sinalphacosbeta)+cosalphasinbeta-cancel(sinalphacosbeta)+cosalphasinbeta#

#=2cosalphasinbeta#