Interesting Discovery?

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(cos⁡30+cos⁡270 ))^2+(3656250(sin⁡30+sin⁡270 ))^2 )

So i figured

a^2 = (a (cos30 + cos270))^2 + (a (sin30 +sin270) )^2

I wanna know how to prove this.

1 answer0 replies

Mar 4

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

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