COMEDK · Maths · 21. Matrices
If \(\left[\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right]\left[\begin{array}{cc}1 & \tan \theta \\ -\tan \theta & 1\end{array}\right]=\left[\begin{array}{cc}a & -b \\ b & a\end{array}\right]\) then
- A \(a=1=b\)
- B \(a=\cos 2 \theta, b=\sin 2 \theta\)
- C \(a=\sin 2 \theta, b=\cos 2 \theta\)
- D \(a=\cos \theta, b=\sin \theta\)
Answer & Solution
Correct Answer
(B) \(a=\cos 2 \theta, b=\sin 2 \theta\)
Step-by-step Solution
Detailed explanation
We have, \(\left[\begin{array}{cc}1 & \tan \theta \\ -\tan \theta & 1\end{array}\right]^{-1}=\frac{1}{1+\tan ^{2} \theta} \quad\left[\begin{array}{cc}1 & -\tan \theta \\ \tan \theta & 1\end{array}\right]\)…
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