CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The maximum value of cosα1.cosα2...... cos αn,
under the restrictions 0α1α2,.....,αnπ2 and cotα1.cotα2......cot αn=1 is

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

The correct option is A
Here(cot α1).(cot α2).....(cot αn)=1
cos α1.cos α2...cos αn=sin α1.sin α2... sin αn
Now, (cos α1.cos α2... cos αn)2
=(cos α1.cos α2... cos αn)=(cos α1.cos α2... cos αn)
=(cos α1.cos α2... cos αn)(sin α1.sin α2... sin αn)
=12nsin 2α1.sin 2α2... sin 2αn.
But each of sin 2α11
(cos α1.cos α2... cos αn)212n.
But each of cos α1 is positive.
cos α1.cos α2.... cos αn12n=12n2.


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