Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

If A = \begin{bmatrix} \cos \theta &i\sin \theta \\ i\sin \theta &\cos \theta \end{bmatrix}, \left ( \theta =\frac{\pi }{24} \right ) and A^{5}=\begin{bmatrix} a &b \\ c& d \end{bmatrix}, where i=\sqrt{-1}, then which of the following is not true?
Option: 1 0\leq a^{2}+b^{2}\leq 1
Option: 2 a^{2}-d^{2}=0
Option: 3 a^{2}-c^{2}=1
Option: 4 a^{2}-b^{2}=\frac{1}{2}
 

Answers (1)

best_answer

A^{2}=\left(\begin{array}{cc} \cos 2 \theta & i \sin 2 \theta \\ \operatorname{isin} 2 \theta & \cos 2 \theta \end{array}\right)

\\\text{Similarly}, A^{5}=\left(\begin{array}{cc}\cos 5 \theta & i \sin 5 \theta \\ i \sin 5 \theta & \cos 5 \theta\end{array}\right)=\left(\begin{array}{ll}a & b \\ c & d\end{array}\right)\\ (1) a^{2}+b^{2}=\cos ^{2} 5 \theta-\sin ^{2} 5 \theta=\cos 10 \theta=\cos 75^{\circ}\\ (2) a^{2}-d^{2}=\cos ^{2} 5 \theta-\cos ^{2} 5 \theta=0 \\(3) a^{2}-b^{2}=\cos ^{2} 5 \theta+\sin ^{2} 5 \theta=1\\ (4) a^{2}-c^{2}=\cos ^{2} 5 \theta+\sin ^{2} 5 \theta=1

Posted by

himanshu.meshram

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
anam-khan

JEE Mains: Farmer's son from remote Maharashtra village aces exam

Latest Question