Question

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

Answer 1

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