Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Determinants
0 votes

Inverse of the matrix $\begin{bmatrix}\cos 2\theta&-\sin 2\theta\\\sin 2\theta&\cos 2\theta\end{bmatrix}$ is

$\begin{array}{1 1}(a)\;\begin{bmatrix}\cos 2\theta&-\sin 2\theta\\\sin 2\theta&\cos 2\theta\end{bmatrix}&(b)\;\begin{bmatrix}\cos 2\theta&\sin 2\theta\\\sin 2\theta&-\cos 2\theta\end{bmatrix}\\(c)\;\begin{bmatrix}\cos 2\theta&\sin 2\theta\\\sin 2\theta&\cos 2\theta\end{bmatrix}&(d)\;\begin{bmatrix}\cos 2\theta&\sin 2\theta\\-\sin 2\theta&\cos 2\theta\end{bmatrix}\end{array}$

Can you answer this question?

1 Answer

0 votes
Inverse of matrix $\begin{bmatrix}a&b\\c&d\end{bmatrix}$
$\Rightarrow \large\frac{1}{ad-bc}$$\begin{bmatrix}d&-b\\c&a\end{bmatrix}$
$4\Rightarrow ad-bc\neq 0$
$A^{-1}=\large\frac{1}{\cos^22\theta+\sin^22\theta}$$\begin{bmatrix}\cos 2\theta&\sin 2\theta\\-\sin 2\theta&\cos 2\theta\end{bmatrix}$
$\Rightarrow \begin{bmatrix}\cos 2\theta&\sin 2\theta\\-\sin 2\theta&\cos 2\theta\end{bmatrix}$
Hence (d) is the correct answer.
answered Nov 22, 2013 by sreemathi.v

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App