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

1 Answer

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

 

answered Feb 20, 2013 by sreemathi.v
edited Feb 24, 2013 by vijayalakshmi_ramakrishnans
 
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