The value of the determinant \(\begin{vmatrix}\sin 30^\circ & \cos 30^\circ\\ -\sin 60^\circ & \cos 60^\circ\end{vmatrix}\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1
Putting in the values \(\sin 30^\circ = \cos 60^\circ = \frac{1}{2}\) and \(\cos 30^\circ = \sin 60^\circ = \frac{\sqrt{3}}{2}\):
\( \displaystyle \Delta = \frac{1}{2} \times \frac{1}{2} - \frac{\sqrt{3}}{2} \times \left(-\frac{\sqrt{3}}{2}\right) \)
\( \displaystyle = \frac{1}{4} + \frac{3}{4} \)
\( = 1 \)
In fact the expansion is \(\sin 30^\circ \cos 60^\circ + \cos 30^\circ \sin 60^\circ = \sin 90^\circ = 1\), by the sine addition formula.