How do you use product to sum formulas to write the product #cos5thetacos3theta# as a sum or difference?

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Answer 1 · 2017-04-25T12:57:35

#cos5thetacos3theta=1/2cos8theta+1/2cos2theta#

As #cos(A+B)=cosAcosB-sinAsinB# and

#cos(A-B)=cosAcosB+sinAsinB#

Adding two, we get #cos(A+B)+cos(A-B)=2cosAcosB#

or #cosAcosB=1/2[cos(A+B)+cos(A-B)]#

Hence, #cos5thetacos3theta#

= #1/2[cos(5theta+3theta)+cos(5theta-3theta)]#

= #1/2cos8theta+1/2cos2theta#