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Let alpha,betaa n dgamma satisfy 0<alpha...

Let `alpha,betaa n dgamma` satisfy `0

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Given, `cos(x+alpha)+cos(x+beta)+cos(x+gamma)=0AAx in R`
`therefore cos x(cos alpha+cosbeta+cos gamma)-sin x(sin alpha+sin beta+sin gamma)`
`=0 AA x in R`
`therefore cos alpha+cos beta+cos gamma=0=sin alpha+sin beta+sin gamma`
`therefore cos alpha+cos gamma=-cos beta`
and `sin alpha+sin gamma=-sin beta`
Squaring Eqs. 1 and 2 and then adding then, we get
`2+2cos(alpha-gamma)=1`
`rArr cos (gamma-alpha)=(-1)/(2)`
`rArr gamma-alpha=(2pi)/(3)` or `(4pi)/(3)`
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