Topic: Engineering Mathematics
The value of the determinant $\begin{vmatrix}\cos~\theta & 0 & \sin~\theta \\ 0 & 1 & 0 \\ -\sin~\theta & 0 & \cos~\theta\end{vmatrix}$ is
- A. 0
- B. -1
- C. 1
- D. 2
Answer: C. 1
Explanation: Expanding the determinant along the second row gives $1\times(\cos\theta\cdot\cos\theta-\sin\theta\cdot(-\sin\theta))$. This simplifies to $\cos^{2}\theta+\sin^{2}\theta$, which is equal to 1 based on standard trigonometric identities.