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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

Grade:12

2 Answers

mycroft holmes
272 Points
7 years ago
 \sec^2 \alpha_1 \sec^2 \alpha_2 ...\sec^2 \alpha_n
 
= (1+\tan^2 \alpha_1) (1+\tan^2 \alpha_2)...(1+\tan^2 \alpha_1)
 
and by AM_GM we have
 
\ge (2 \tan \alpha_1) (2 \tan \alpha_2)...(2 \tan \alpha_n)
 
= 2^n \tan \alpha_1 \tan \alpha_2...\tan \alpha_n
 
= 2^n
 
It follows that the max value of the given expression is \boxed{\frac{1}{2^{\frac{n}{2}}}}
 
Dheeraj
39 Points
5 years ago
For maximum vaule
 
Cotx1=cotx2=......….........=π⁄4
So max value of 
Cosx1.cosx2 .....=(1/√2)^n
                             Thankyou

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