the maxm value of cosa_1*cosa2*..... cosa_{n under the restriction (0<=a1,a2,.......an<=90 and cot a1*cota2....cotan=1) is.........}

Dear nishant

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

so cosa_1,cosa2,..... cosa_n  all are positive .

use AM ≥GM

 ( cosa₁₊ cosa2+  .....+  cosa_n)/n ≥[cosa_1*cosa2*..... cosa_n]^1/n

equality occure when all are equal

  cosa₁₌ cosa2=  .....=  cosa_n

so a1 =a2=a3 =   =an

but given

cot a1*cota2....cotan=1

 (cota1)ⁿ=1

  cota1= 1

       a1=45

so

cosa_1*cosa2*..... cosa_{n =}(cosa1)ⁿ ₌ (1/√2)ⁿ

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