I was just adding vectors and I stumble upon this equality
1 = sqrt((cos30 + cos270))^2 + ((sin30 +sin270) )^2 )
2 = sqrt( (2 (cos30 + cos270))^2 + (2 (sin30 +sin270) )^2 )
3656250=sqrt((3656250(cos30+cos270 ))^2+(3656250(sin30+sin270 ))^2 )
So i figured
a^2 = (a (cos30 + cos270))^2 + (a (sin30 +sin270) )^2
I wanna know how to prove this.
a^2[cos(30) + cos(270)] ^2 + a^2[sin(30) + sin(270)]^2
=a^2[sqrt(3)/2 + 0]^2 + a^2[1/2 + (-1)]^2
= a^2[sqrt(3)/2 ]^2 + a^2[-1/2]^2
= a^2[3/4] + a^2[1/4]
= a^2[3/4 + 1/4]
= a^2