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  4. Evaluate | cos 15 sin 15 sin 75 cos 75|

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Q. Evaluate $\begin{vmatrix}\cos 15 & \sin 15 \\ \sin 75 & \cos 75\end{vmatrix}$

KCETKCET 2015Determinants

Solution:

$\begin{vmatrix} {\cos 15}&{\sin 15} \\ {\sin 75}&{\cos 75} \end{vmatrix} $
$= \cos 15 \cos 75 - \sin 15 \sin 75 $
$= \cos (15 + 75) = \cos\, 90 = 0$