Math CentralQuandaries & Queries


Subject: Question
Name: saban

Who are you: Other

cos 2a+cos4a+cos6a=?

Hi Saban,

You haven't given us the instruction s for this problem but you are probably looking to write this expression in terms of sin a and cos a. To accomplish this you need to use the identities

cos(p + q) = cos(p) cos(q) - sin(p) sin(u)


sin(p + q) = sin(p) cos(q) + cos(p) sin(q)

Penny and Stephen La Rocque.


There are many choices for identities here. For example, you can write the cosine of an even multiple of 'a' as a polynomial in (cos a)^2. To make it easier to read, I will let x = (cos a)^2. By using basic trig identities and a lot of patience you can easily see that

cos 2a = 2x - 1
cos 4a = 8 x^2 - 8x + 1
cos 6a = 32 x^3 - 48 x^2 +18x - 1


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