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35. The maximum value of (cos α1 ). (cos α2 ). ….. (cos αn ), under the restrictions 0 ≤ α1,α2,……,αn ≤ π/2 and (cot α1 ). (cot α2 ). ….. (cot αn )=1 is: (A) 1/2n⁄2 (B) 1/2n (C) 1/2n (D) 1 35. The maximum value of (cos α1 ). (cos α2 ). ….. (cos αn ), under the restrictions 0 ≤ α1,α2,……,αn ≤ π/2 and (cot α1 ). (cot α2 ). ….. (cot αn )=1 is: (A) 1/2n⁄2 (B) 1/2n (C) 1/2n (D) 1
and by AM_GM we have It follows that the max value of the given expression is
For maximum vaule Cotx1=cotx2=......….........=π⁄4So max value of Cosx1.cosx2 .....=(1/√2)^n Thankyou
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