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?

Answered by mr W last updated on 29/Mar/21

A = π - (B + C)

y = - 2 \cos (B + C) + \cos B + \cos C

d u e t o s y m m e t r y : B = C = x

y = - 2 \cos 2 x + 2 \cos x

y = - 4 \cos^{2} x + 2 + 2 \cos x)

y = \frac{9}{4} - (4 \cos^{2} x - 2 \cos x + \frac{1}{4})

y = \frac{9}{4} - {(2 \cos x - \frac{1}{2})}^{2}

y_{m a x} = \frac{9}{4} w h e n B = C = x = \cos^{- 1} \frac{1}{4}

Commented by bobhans last updated on 29/Mar/21

why B and C symetri sir

Commented by mr W last updated on 29/Mar/21

i n t h e f u n c t i o n

y = - 2 \cos (B + C) + \cos B + \cos C

y o u c a n e x c h a n g e B a n d C a n d t h e

f u n c t i o n r e m a i n s t h e s a m e . w h e n

s u c h a f u n c t i o n h a s m a x i m u m o r

m i n i m u m, t h e n B = C .

Facebook Tweet Pin