How can the sum of three cosines equal 1?

[Gunthi]

Hi there,

I'm trying to figure out how the sum of three cosines exposed in page 2 of:
http://www.mrl.ucsb.edu/~seshadri/2004_100A/100A_MillerBragg.pdf
can be proved...

Any help would be appreciated...

Thanks in advance,
G.

 

[Norwegian]

If OP=d, the coordinates of P are (cos α₁,cos α₂,cos α₃)d. Now, express the length of OP using Pythagoras and you get the desired relation.

 

[Gunthi]

If OP=d, the coordinates of P are (cos α₁,cos α₂,cos α₃)d. Now, express the length of OP using Pythagoras and you get the desired relation.

Got it! Thanks!