A) if \[a=b\]or\[\theta =n\pi ,\]where is an integer
B) Always
C) Never
D) if \[a\,\cos \theta \ne b\sin \theta \]
Correct Answer: A
Solution :
| \[\left[ \begin{align} & \cos \theta -\sin \theta \\ & \sin \theta -\cos \theta \\ \end{align} \right]\left[ \begin{align} & a\,\,0 \\ & 0\,\,b \\ \end{align} \right]=\left[ \begin{align} & a\,\cos \theta -b\sin \theta \\ & a\sin \theta -b\cos \theta \\ \end{align} \right]\] |
| and |
| \[\left[ \begin{align} & a\,\,0 \\ & 0\,\,b \\ \end{align} \right]=\left[ \begin{align} & \cos \theta -\sin \theta \\ & \sin \theta -\cos \theta \\ \end{align} \right]=\left[ \begin{align} & a\,\cos \theta -a\sin \theta \\ & b\sin \theta \,b\cos \theta \\ \end{align} \right]\] |
| \[a\,\sin \theta =b\sin \theta \Rightarrow (a-b)sin\theta =0\] |
| Either a=b\[or\sin \theta =0\Rightarrow \theta =n\pi ;n\in \mathbb{Z}\] |
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