Yoshitaka Ikeda <ikeda@4bn.ne.jp> wrote in message news:<ca9564$eai$1@caraway.media.kyoto-u.ac.jp>...
> ronさんの<c9sjf1$2fh$1@inews.gazeta.pl>から
> >how can I simplify
> >
> >sin(x) + sin(2x) + sin(3x)
> >cos(x) + cos(2x) + cos(3x)
> >
> >greetings
> 
> sin(x) can be written sin(2x-x)
> sin(3x) can be written sin(2x+x)
> So, 
> sin(x)=sin(2x)cos(x)-cos(2x)sin(x)
> and 
> sin(3x)=sin(2x)cos(x)+cos(2x)sin(x)
> 
> So,
> sin(x)+sin(2x)+sin(3x)=sin(2x)(2cos(x)+1)
> 
> 
> In a similar way
> cos(x)=cos(2x-x)=cos(2x)cos(x)+sin(2x)sin(x)
> cos(3x)=cos(2x+x)=cos(2x)cos(x)-sin(2x)sin(x)
> 
> cos(x)+cos(2x)+cos(3x)=cos(2x)(2cos(x)+1)


However, "sin(x) + sin(2x) + sin(3x)"looks more simple than"sin(2x)(2cos(x)+1)"
isn't it ?