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Trigometric Proof

by es801
Tags: algebra, proof, trigonometry
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es801
#1
Jun12-11, 09:52 AM
P: 1
I am having trouble proving the following trigonometric equation:
cosx + cos3x +cos5x = sin6x/2sinx

Any help would be appreciated
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eumyang
#2
Jun12-11, 10:15 AM
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P: 1,347
You'll need to show us your attempt before we can help you. I assume that you are familiar with the trigonometric identities (particularly, the sum/difference & multiple-angle identities).
ehild
#3
Jun12-11, 02:40 PM
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P: 10,661
Are you familiar with complex numbers and Euler's formula?

ehild

QuarkCharmer
#4
Jun12-11, 03:45 PM
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Trigometric Proof

Quote Quote by ehild View Post
Are you familiar with complex numbers and Euler's formula?

ehild
They don't teach those in general trigonometry. Though that would work (as it usually does).

Since this is in terms of x, I would try to use the identity (sin(x+x))= ... to get the whole thing in terms of single variables. For example sin(5x) is really sin(4x+x) which can expand, and then sin(3x+1) expands out and so on. Then it should be easy to simplify.
ehild
#5
Jun17-11, 01:26 PM
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Try to write both sides in terms of cos(3x) and cos(x), using the addition rules. (x=3x-2x, 5x=3x+2x, 6x=2*(3x) ).

ehild


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