Question

The value of $\Delta =\left|\begin{array}{cc}\cos {15}^{\circ }& \sin {15}^{\circ }\\ \sin {75}^{\circ }& \cos {75}^{\circ }\end{array}\right|$ is

[2 marks]

• A. $1$
• B. $\cos {60}^{\circ }$
• C. $\cos {80}^{\circ }$
• D. $0$

Answer 1

The correct option is D $0$

$\Delta =\left|\begin{array}{cc}\cos {15}^{\circ }& \sin {15}^{\circ }\\ \sin {75}^{\circ }& \cos {75}^{\circ }\end{array}\right|$
$\Rightarrow \Delta =\cos {15}^{\circ }\cos {75}^{\circ }-\sin {15}^{\circ }\sin {75}^{\circ }$
$\Rightarrow \Delta =\cos ({15}^{\circ }+{75}^{\circ })$
$(\because \cos (a+b)=\cos a\cos b-\sin a\sin b)$
$\Rightarrow \Delta =\cos {90}^{\circ }$
$\therefore \Delta =0$