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

If acos3α+3acosαsin2α=m and asin3α+3acos2αsinα=n, then (m+n)23+(mn)23=

A
2a2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2a13
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
2a23
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
2a3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 2a23

Adding and subtracting the given relation,

we get (m+n)=acos3α+3acosαsin2α+3acos2αsinα+asin3α

=a(cosα+sinα)3

and similarly (mn)=a(cosαsinα)3

Thus, (m+n)23+(mn)23

=a23{(cosα+sinα)2+(cosαsinα)2}

=a23{2(cos2α+sin2α)}=2a23


flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Conditional Identities
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon