wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

If 0<θ<π2 and x=n=0cos2nθ,y=n=0sin2nθ,z=n=0cos2nθsin2nθ, then the value of xyz is

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

The correct option is B x+y+z

x=1+cos2θ+cos4θ+...
Hence sum of G.P is
=11cos2θ
=1sin2θ
y=1+sin2θ+sin4θ+...
Hence sum of G.P is
=11sin2θ

=1cos2θ

z=1+cos2θ.sin2θ+cos4θ.sin4θ...

=11cos2θ.sin2θ
Hence x.y.z
=1cos2θ.sin2θ.11cos2θ.sin2θ

=1cos2θ.sin2θ(1cos2θ.sin2θ)

=1cos2θ.sin2θ+cos2θ.sin2θcos2θ.sin2θ(1cos2θ.sin2θ)

=1cos2θ.sin2θ+11cos2θ.sin2θ

=cos2θ+sin2θcos2θ.sin2θ+11cos2θ.sin2θ

=1cos2θ+1sin2θ+11cos2θ.sin2θ

=x+y+z


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