SOLUTION: cos5xcos2x+sin5xsin2x= -1 for x is greater or equal to 0, and less than or equal to 2pi

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Question 964658: cos5xcos2x+sin5xsin2x= -1 for x is greater or equal to 0, and less than or equal to 2pi
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Use the identity,
cos%28x-y%29=cos%28x%29cos%28y%29%2Bsin%28x%29sin%28y%29
.
.
cos%285x-2x%29=-1
cos%283x%29=-1
3x%2B2pi%2Ak=pi
x=pi%2F3%2B%282%2F3%29pi%2Ak
x=%281%2F3%29pi<-- k=0
x=%283%2F3%29pi=pi<-- k=1
x=%285%2F3%29pi<-- k=2