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nishant kumar agarwal Grade: Upto college level
        

the maxm value of cosa1*cosa2*..... cosan under the restriction (0<=a1,a2,.......an<=90 and cot a1*cota2....cotan=1) is.........

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear nishant


0<=a1,a2,.......an<=90


so cosa1,cosa2,..... cosaall 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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Badiuddin



7 years ago
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