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)

-- 
Yoshitaka Ikeda mailto:ikeda@4bn.ne.jp