SOLUTION: 44. verify the identiy cos(x+y)+cos(x-y)=2cosxcosy

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Question 174443: 44. verify the identiy
cos(x+y)+cos(x-y)=2cosxcosy
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm only manipulating the left side. I'm NOT changing the right side. I'm showing the right side for comparison.



cos(x+y)+cos(x-y)=2cos(x)*cos(y) ... Start with the given equation


[cos(x)cos(y)-sin(x)sin(y)]+cos(x-y)=2cos(x)*cos(y) ... Expand cos(x+y)



[cos(x)cos(y)-sin(x)sin(y)]+[cos(x)cos(y)+sin(x)sin(y)]=2cos(x)*cos(y) ... Expand cos(x-y)



[cos(x)cos(y)+cos(x)cos(y)]]+[sin(x)sin(y)-sin(x)sin(y)]=2cos(x)*cos(y) ... Group like terms.


2cos(x)*cos(y)=2cos(x)*cos(y) ... Combine like terms. So this verifies the given identity