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 first row: $cos~\theta[1\cdot cos~\theta - 0] - 0 + sin~\theta[0 - 1(-sin~\theta)] = cos^{2}\theta + sin^{2}\theta = 1$.