Question

Find the value of the determinant $\left|\begin{array}{ccc}1& 0& 0\\ 2& \cos x& \sin x\\ 3& \sin x& \cos x\end{array}\right|$.

• A. $\cos 2x$
• B. $1$
• C. $0$
• D. $\sin 2x$

Answer 1

Answer: (A)

$\cos 2x$

Given

$\left|\begin{array}{ccc}1& 0& 0\\ 2& cosx& sinx\\ 3& sinx& cosx\end{array}\right|$

$=1(\cos x\times \cos x-\sin x\times \sin x)$

$={\cos }^x-{\sin }^{2}x$

We know that

$\cos 2x={\cos }^{2}x-{\sin }^{2}x$

$=\cos 2x$