Solve determinants : left|begin{array}{ll}cos θ & -sin θ sin θ & cos θend{array}right|

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3 and 4 .Determinants and Matrices

easy

Evaluate the determinants : $\left|\begin{array}{ll}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right|$

A

$0$

B

$-1$

C

$1$

D

$2$

Solution

$\left| {\begin{array}{*{20}{c}}
{\cos \theta }&{ – \sin \theta } \\
{\sin \theta }&{\cos \theta }
\end{array}} \right|$

$ = (\cos \theta )(\cos \theta ) – ( – \sin \theta )(\sin \theta )$

$ = {\cos ^2}\theta + {\sin ^2}\theta $

$ = 1$

Standard 12

Mathematics

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