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  4. |cos 15°&sin 15° sin 75°&cos 75°|=

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Q. $\begin{vmatrix}cos\,15^{\circ}&sin\,15^{\circ}\\ sin\,75^{\circ}&cos\,75^{\circ}\end{vmatrix}=$

Determinants

Solution:

We have
$\begin{vmatrix}cos\,15^{\circ}&sin\,15^{\circ}\\ sin\,75^{\circ}&cos\,75^{\circ}\end{vmatrix}=$
$=cos\, 75^{\circ} \,cos 15^{\circ}-sin \,75^{\circ} \,sin \,15^{\circ}=cos \left(75^{\circ}+15^{\circ}\right)$
$=cos \,90^{\circ}=0$