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

The number of distinct real roots of
∣ ∣sin xcos xcos xcos xsin xcos xcos xcos xsin x∣ ∣=0 in the interval π4xπ4 is

A
\N
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
3
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 1
Given, ∣ ∣sin xcos xcos xcos xsin xcos xcos xcos xsin x∣ ∣=0
Applying C1C1+C2+C3
=∣ ∣sin x+2 cos xcos xcos xsin x+2 cos xsin xcos xsin x+2 cos xcos xsin x∣ ∣
=(2 cos x+sin x)∣ ∣1cos xcos x1sin xcos x1cos xsin x∣ ∣=0
Applying R2R2R1, R3R3R1
(2 cos x+sin x)∣ ∣1cos xcos x0sin xcos x000sin xcos x∣ ∣=0 (2 cos x+sin x)(sin xcos x)2=0
2 cos x + sin x = 0 or sin x - cos x = 0
2 cos x =-sin x or sin x = cos x
cot x=12 gives no solution in π4xπ4
and sin x = cos x tan x = 1 x=π4

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