Question 194974
I'd start with the left side and work my way to get it equal to the right side (if you go with the left side, do NOT change the right).



Recall the identities:


cos(A+B) = cos(A)cos(B)-sin(A)sin(B), and



cos(A-B) = cos(A)cos(B)+sin(A)sin(B)



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cos(A+B)+cos(A-B)=2cos(A)cos(B) ... Start with the given equation.



[cos(A)cos(B)-sin(A)sin(B)]+cos(A-B)=2cos(A)cos(B) ... Use the first identity given above



[cos(A)cos(B)-sin(A)sin(B)]+[cos(A)cos(B)+sin(A)sin(B)]=2cos(A)cos(B) ... Use the second identity given above



[cos(A)cos(B)+cos(A)cos(B)]+[-sin(A)sin(B)+sin(A)sin(B)]=2cos(A)cos(B) ... Rearrange the terms.



2cos(A)cos(B)+0=2cos(A)cos(B) ... Combine like terms.



2cos(A)cos(B)=2cos(A)cos(B) ... Simplify



Since both sides are equal, we've verified the identity.