KCET · Maths · Three Dimensional Geometry
Evaluate \( \left|\begin{array}{cc}\cos 15 & \sin 15 \\ \sin 75 & \cos 75\end{array}\right| \)
- A \( 1 \)
- B \( 00 \)
- C \( 12 \)
- D \( 13 \)
Answer & Solution
Correct Answer
(B) \( 00 \)
Step-by-step Solution
Detailed explanation
Given that,
\[
\begin{array}{l}
\left|\begin{array}{l}
\cos 15^{\circ} \sin 15^{\circ} \\
\sin 75^{\circ} \cos 75^{\circ}
\end{array}\right| \\
=\cos 15^{\circ} \cos 75^{\circ}-\sin 15^{\circ} \sin 75^{\circ} \\
=\cos \left(15^{\circ}+75^{\circ}\right)=\cos \left(90^{\circ}\right)=0
\end{array}
\]
\[
\begin{array}{l}
\left|\begin{array}{l}
\cos 15^{\circ} \sin 15^{\circ} \\
\sin 75^{\circ} \cos 75^{\circ}
\end{array}\right| \\
=\cos 15^{\circ} \cos 75^{\circ}-\sin 15^{\circ} \sin 75^{\circ} \\
=\cos \left(15^{\circ}+75^{\circ}\right)=\cos \left(90^{\circ}\right)=0
\end{array}
\]
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