Question

The value of the determinat $\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right|$ is .

• A. $2{\sin }^2\theta$
• B. $2{\cos }^2\theta$
• C. $0$
• D. $1$

Answer 1

The correct option is D $1$

$\left(\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{array}\right|=\cos \theta \left(\cos \theta \right)-\sin \theta \left(-\sin \theta \right)={\cos }^2\theta +{\sin }^2\theta =1$