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#1

$Old$ November 7th, 2009, 12:55 AM

jut $jut is offline$

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$Default$ 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

$Old$ November 7th, 2009, 01:03 AM

Gusbob $Gusbob is offline$

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Does this help?

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#3

$Old$ November 7th, 2009, 01:06 AM

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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

$Old$ November 7th, 2009, 01:15 AM

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Yeah I got it from wiki. Couldn't bear to type up so much.

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