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Given-triangle-ABC-what-is-the-maximum-value-of-y-2cosA-cosB-cosC-




Question Number 137038 by bobhans last updated on 29/Mar/21
  Given triangle ABC, what is the maximum value of y=2cosA + cosB + cosC?
Given triangle ABC, what is the maximum value of y=2cosA + cosB + cosC?
Answered by mr W last updated on 29/Mar/21
A=π−(B+C)  y=−2 cos (B+C)+cos B+cos C  due to symmetry: B=C=x  y=−2 cos 2x+2 cos x  y=−4 cos^2  x+2+2 cos x)  y=(9/4)−(4 cos^2  x−2 cos x+(1/4))  y=(9/4)−(2 cos x−(1/2))^2   y_(max) =(9/4) when B=C=x=cos^(−1) (1/4)
A=π(B+C)y=2cos(B+C)+cosB+cosCduetosymmetry:B=C=xy=2cos2x+2cosxy=4cos2x+2+2cosx)y=94(4cos2x2cosx+14)y=94(2cosx12)2ymax=94whenB=C=x=cos114
Commented by bobhans last updated on 29/Mar/21
why B and C symetri sir
whyBandCsymetrisir
Commented by mr W last updated on 29/Mar/21
in the function  y=−2 cos (B+C)+cos B+cos C  you can exchange B and C and the  function remains the same. when   such a function has maximum or   minimum, then B=C.
inthefunctiony=2cos(B+C)+cosB+cosCyoucanexchangeBandCandthefunctionremainsthesame.whensuchafunctionhasmaximumorminimum,thenB=C.

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