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Math Help - Simplify this trig expression

  1. #1
    jut
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    Simplify this trig expression

    (\sin(x)+\sin(2x)+\sin(3x)+\sin(4x)+\sin(5x))^2 +(\cos(x)+\cos(2x)+\cos(3x)+\cos(4x)+\cos(5x)+1)^2

    I was able to do with the brute force way, that is, multiply everything out then use the identity: cos(a-b)=cos(a)cos(b)+sin(a)sin(b) to reduce everything to:

    6+10 cos(x)+8 cos(2x)+6 cos(3x)+4 cos(4x)+2 cos(5 x)

    My question is: is there a more elegant way to do this that doesn't take 5 YEARS.
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  2. #2
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    Does this help?




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  3. #3
    jut
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    Hmm that looks interesting

    You got that from here: List of trigonometric identities - Wikipedia, the free encyclopedia
    right?

    I was browsing that earlier and looked over it. Thank you sir!
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  4. #4
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    Yeah I got it from wiki. Couldn't bear to type up so much.
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