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cosx+cosy+cosz=0=sinx+siny+sinz then prove cos(x+y)+cos(y+z)+cos(z+x)=0

cosx+cosy+cosz=0=sinx+siny+sinz then prove cos(x+y)+cos(y+z)+cos(z+x)=0

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
cos(θ − x) + cos(θ − y) + cos(θ − z)
= cos θ cos x + sin θ sin x + cos θ cos y + sin θ sin y + cos θ cos z + sin θ sin z
= cos θ[cos x + cos y + cos z] + sin θ[sin x + sin y + sin z]
= 0
Setting θ = x + y + z in (b), we get cos(x + y) + cos(y + z) + cos(x + z) = 0.

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