The value of $\left|\begin{array}{llr}\sin 15° & \cos 15° & 2 \sin 30° \\ \sin 30° & \cos 30° & \sin 45° \\ \cos 75° & \sin 75° & \sin 90°\end{array}\right|$ is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0
$\left|\begin{array}{llr}\sin 15° & \cos 15° & 2 \sin 30° \\ \sin 30° & \cos 30° & \sin 45° \\ \cos 75° & \sin 75° & \sin 90°\end{array}\right|$
$=\sin 15°(\cos 30°\sin 90°-\sin 75°\sin 45°)-\cos 15°(\sin 30°\sin 90°-\cos 75°\sin 45°)+2\sin 30°(\sin 30°\sin 75°-\cos 75°\cos 30°)$
$=0$