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the maxm value of cosa1*cosa2*..... cosan under the restriction (0<=a1,a2,.......an<=90 and cot a1*cota2....cotan=1) is.........
Dear nishant
0<=a1,a2,.......an<=90
so cosa1,cosa2,..... cosan all are positive .
use AM ≥GM
( cosa1+ cosa2+ .....+ cosan)/n ≥[cosa1*cosa2*..... cosan]1/n
equality occure when all are equal
cosa1= cosa2= .....= cosan
so a1 =a2=a3 = =an
but given
cot a1*cota2....cotan=1
(cota1)n=1
cota1= 1
a1=45
so
cosa1*cosa2*..... cosan =(cosa1)n = (1/√2)n
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