Question

Assest the validity of the following statement: For all integrals m & n with m is opposite of -n & +n, and integral (cosm(t)cosn(t)dt)=0 from -pi to pi ???

Answer 1

hey one sec i did this before

Answer 2

let me see if i can find it

Answer 3

yeaaaaaaay

Answer 4

can't wait because i don't even understand the question

Answer 5

lol

Answer 6

http://openstudy.com/users/myininaya#/users/myininaya/updates/4e6977100b8b4a2b95d0ce28

Answer 7

wooww and how do you know that "we also know that thing?"

Answer 8

i was just using identities
we have
\[\cos(x+y)=\cos(x)\cos(y)-\sin(x)\sin(y)\]
and
\[\cos(x-y)=\cos(x)\cos(y)+\sin(x)\sin(y)\]

adding these equations together we get

\[\cos(x+y)+\cos(x-y)=2\cos(x)\cos(y)+0\]
\[\cos(x+y)+\cos(x-y)=2\cos(x)\cos(y)\]

Answer 9

multiply 1/2 on both sides and get
\[\frac{1}{2}[\cos(x+y)+\cos(x-y)]=\cos(x)\cos(y)\]

Answer 10

\[\cos(x)\cos(y)=\frac{1}{2}[\cos(x+y)+\cos(x-y)]\]

\[\cos(m \theta) \cos(n \theta)=\frac{1}{2}[\cos(m \theta+n \theta)+\cos(m \theta- n \theta)]\]
\[\cos(m \theta) \cos(n \theta)=\frac{1}{2}[\cos([m+n] \theta)+\cos([m-n] \theta)]\]

Answer 11

so is this the answer ? or that one

Answer 12

what do you mean?

Answer 13

i went through the whole thing on the other thread
i just put some more steps on this one because you asked
so what do you mean which is the answer?

Answer 14

ohh okk got it. thank youu!

Answer 15

the whole thing from both threads is the answer
this is a proof