SOLUTION: use sum or difference formula to find exact value of the following: cos(5pi/7)cos(23pi/42) + sin(5pi/7)sin(23pi/42)

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Question 1063574: use sum or difference formula to find exact value of the following: cos(5pi/7)cos(23pi/42) + sin(5pi/7)sin(23pi/42)
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
cos(5pi/7)cos(23pi/42) + sin(5pi/7)sin(23pi/42)

Use the identity

cos%28alpha-beta%29%22%22=%22%22cos%28alpha%29cos%28beta%29+%2B+sin%28alpha%29sin%28beta%29

where alpha=%285pi%29%2F7 and beta=23pi%2F42

cos%28%285pi%29%2F7-%2823pi%29%2F42%29%29%22%22=%22%22

cos%28%286%285pi%29%29%2F%286%2A7%29-%2823pi%29%2F42%29%22%22=%22%22

cos%28%2830pi%29%2F42-%2823pi%29%2F42%29%22%22=%22%22

cos%28%287pi%29%2F42%29%22%22=%22%22

cos%28pi%2F6%29%22%22=%22%22

sqrt%283%29%2F2

Edwin