Question

Evaluate the following determinants,
$\left|\begin{array}{cc}cos15^{\circ }& sin15^{\circ }\\ sin75^{\circ }& cos75^{\circ }\end{array}\right|$

• A. $0$
• B. $5$
• C. $3$
• D. $7$

Answer 1

Answer: (A)

We have, $\left|\begin{array}{cc}cos15^{\circ }& sin15^{\circ }\\ sin75^{\circ }& cos75^{\circ }\end{array}\right|$
$cos75^{\circ }cos15^{\circ }-sin75^{\circ }sin15^{\circ }$
$=cos\left(75^{\circ }+15^{\circ }\right)=cos90^{\circ }=0$