SOLUTION: How do you verify cos(A+B)+cos(A-B)=2cosAcosB

Click here to see ALL problems on Trigonometry-basics

Question 194974: How do you verify cos(A+B)+cos(A-B)=2cosAcosB
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
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)

--------------------------------------------------

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.