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

Assertion :The system of linear equations x+(sinα)y+(cosα)z=0x+(cosα)y+(sinα)z=0x+(sinα)y(cosα)z=0 has a non trivial solution for only one value of α lying between 0 and π. Reason: ∣ ∣sinxcosxcosxcosxsinxcosxcosxcosxsinx∣ ∣=0 has no solution in the interval π4<x<π4.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
Assertion is correct but Reason is incorrect
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
Assertion is incorrect but Reason is correct
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
Given system of linear equations x+(sinα)y+(cosα)z=0x+(cosα)y+(sinα)z=0x+(sinα)y(cosα)z=0
For non-trivial solution,
∣ ∣1sinαcosα1cosαsinα1sinαcosα∣ ∣=0
2sin2α+2sinαcosα=0
either sinα=0 or tanα=1
α=π4(as0<α<π)
Hence, the statement 1 is true.
For statement 2, given ∣ ∣sinxcosxcosxcosxsinxcosxcosxcosxsinx∣ ∣=0
C1C1+C2+C3
(sinx+2cosx)∣ ∣1cosαcosα1sinαcosα1cosαsinα∣ ∣=0
(sinx+2cosx)(cosxsinx)2=0
(sinx+2cosx)(cosxsinx)2=0
tanx=2,tanx=1
Since, π4<x<π4
1<tanx<1
Hence, there is no solution for the given system of equations (determinant).
Hence, reason is also true.But reason is not the correct explanation for assertion.

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