wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Adjoint of a Matrix
The value of ...
Question

The value of ⎡⎢ ⎢ ⎢⎣1−tanθ4tanθ41⎤⎥ ⎥ ⎥⎦⎡⎢ ⎢ ⎢⎣1tanθ4−tanθ41⎤⎥ ⎥ ⎥⎦−1 is

A
⎡⎢ ⎢ ⎢⎣cosθ2sinθ2−sinθ2cosθ2⎤⎥ ⎥ ⎥⎦
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
⎡⎢ ⎢ ⎢⎣cosθ2−sinθ2sinθ2cosθ2⎤⎥ ⎥ ⎥⎦
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
⎡⎢ ⎢ ⎢⎣sinθ2cosθ2−cosθ2sinθ2⎤⎥ ⎥ ⎥⎦
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
⎡⎢ ⎢ ⎢⎣sinθ2−cosθ2cosθ2sinθ2⎤⎥ ⎥ ⎥⎦
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A ⎡⎢ ⎢ ⎢⎣cosθ2−sinθ2sinθ2cosθ2⎤⎥ ⎥ ⎥⎦
=⎡⎢ ⎢ ⎢⎣1−tanθ4tanθ41⎤⎥ ⎥ ⎥⎦1(1+tan2θ4)⎡⎢ ⎢ ⎢⎣1−tanθ4tanθ41⎤⎥ ⎥ ⎥⎦

=1sec2θ4⎡⎢ ⎢ ⎢⎣1−tanθ4tanθ41⎤⎥ ⎥ ⎥⎦⎡⎢ ⎢ ⎢⎣1−tanθ4tanθ41⎤⎥ ⎥ ⎥⎦

=cos2θ4⎡⎢ ⎢ ⎢⎣1−tan2θ4−2tanθ42tanθ41−tan2θ4⎤⎥ ⎥ ⎥⎦

=cos2θ4⎡⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢⎣cos2θ4−sin2θ4cos2θ4−2sinθ4cosθ42sinθ4cosθ4cos2θ4−sin2θ4cos2θ4⎤⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥⎦

=⎡⎢ ⎢ ⎢⎣cosθ2−sinθ2sinθ2cosθ2⎤⎥ ⎥ ⎥⎦

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Adjoint and Inverse of a Matrix
MATHEMATICS
Watch in App
explore_more_icon
Explore more
Adjoint of a Matrix
Standard XII Mathematics
Join BYJU'S Learning Program
book_image
AI Tutor
book_image
Textbooks
book_image
Question Papers
book_image
Install app
CrossIcon