Question

Evaluate: $\left|\begin{array}{cc}\cos 15°& \sin 15°\\ \sin 75°& \cos 75°\end{array}\right|$

Answer 1

$$\begin{gathered} \left|\cos 15°\sin 15° \\ \sin 75°\cos 75°\right| \\ =\cos 15°\cos 75°-\sin 15°\sin 75° \\ =\cos (15°+75°)\left[\because \cos A\cos B-\sin A\sin B=\cos (A+B)\right] \\ =\cos 90° \\ =0 \\ \Rightarrow \left|\cos 15°\sin 15° \\ \sin 75°\cos 75°\right|=0 \end{gathered}$$