Question

Evaluate the following determinants,
$\left|\begin{matrix}cos\, 15^{\circ}&sin\, 15^{\circ}\\ sin \, 75^{\circ}&cos \, 75^{\circ}\end{matrix}\right|$

• A. $0$
• B. $5$
• C. $3$
• D. $7$

Answer 1

Answer: (A)

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