wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The maximum value of (cosα1).(cosα2)...(cosαn), under the restrictions 0α1,α2,...αnπ2 and (cotα1).(cotα2)...(cotαn)=1 is :

A
12n2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
12n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
12n
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

Given condition:

(cotα1).(cotα2)...(cotαn)=1

ni=1cotαi=1

ni=1cosαini=1sinαi=1

ni=1cosαi=ni=1sinαi)

cosα1cosα2cosα3....cosαn=sinα1sinα2sinα3.....sinαn

This is possible only if α1=α2=α3=α4....=αn=π4

Now, the maximum value of cosα1cosα2cosα3....cosαn

=cosπ4cosπ4cosπ4....cosπ4

=12.12.12.12....n-times

=(12)n

=(1212)n

=12n2

cosα1cosα2cosα3....cosαn=12n2

Hence, Option A is correct.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon