Browse Questions

# Evaluate : $\begin{vmatrix} cos \theta & -sin \theta \\ sin \theta & cos \theta \end{vmatrix}$

Toolbox:
• To evaluate the value of the given determinants ,let us multiply the elements $a_{11}$ and $a_{22}$ and then subtract $a_{21}\times a_{12}$.
$A=\begin{vmatrix}cos\theta &-sin\theta\\sin\theta & cos\theta\end{vmatrix}$
let us multiply the elements $a_{11}$ and $a_{22}$ and then subtract $a_{21}\times a_{12}$.
We get,
$\mid A\mid=\cos \theta\times \cos\theta-(\sin\theta)\sin\theta$.
$\qquad=\cos^2\theta+\sin^2\theta$
But $cos^2\theta+sin^2\theta$=1.
Therefore $\mid A\mid=1.$