Question

Evaluate $\left|\begin{array}{cc}\cos {15}^o& \sin {15}^o\\ \sin {75}^o& \cos {75}^o\end{array}\right|$

• A. $1$
• B. $0$
• C. $2$
• D. $3$

Answer 1

The correct option is B $0$

Using fundamental theorem of determinant,

$\left|\begin{array}{cc}\cos {15}^o& \sin {15}^o\\ \sin {75}^o& \cos {75}^o\end{array}\right|=\cos {15}^o\cos {75}^o-\sin {15}^0\sin {75}^o$

$=\cos ({75}^o+{15}^o)=\cos {90}^o=0$, [using sum to product formula]

We have used the Fundamental theorem of determinant is $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-bc$