Q84 / 180 · KCET 2015 · Mathematics
Evaluate \( \left|\begin{array}{cc}\cos 15 & \sin 15 \\ \sin 75 & \cos 75\end{array}\right| \)
- A\( 1 \)
- Correct answerB\( 00 \)
- C\( 12 \)
- D\( 13 \)
Solution
Given that,
\[ \begin{array}{l} \left|\begin{array}{l} \cos 15^{\circ} \sin 15^{\circ} \\ \sin 75^{\circ} \cos 75^{\circ} \end{array}\right| \\ =\cos 15^{\circ} \cos 75^{\circ}-\sin 15^{\circ} \sin 75^{\circ} \\ =\cos \left(15^{\circ}+75^{\circ}\right)=\cos \left(90^{\circ}\right)=0 \end{array} \]
\[ \begin{array}{l} \left|\begin{array}{l} \cos 15^{\circ} \sin 15^{\circ} \\ \sin 75^{\circ} \cos 75^{\circ} \end{array}\right| \\ =\cos 15^{\circ} \cos 75^{\circ}-\sin 15^{\circ} \sin 75^{\circ} \\ =\cos \left(15^{\circ}+75^{\circ}\right)=\cos \left(90^{\circ}\right)=0 \end{array} \]
Hence, the correct answer is option: 'B'.