Find the determinant of \(\begin{vmatrix} sinx & cosx \\ -cosx & sinx \end{vmatrix}\).

Solution :

Let | A | = \(\begin{vmatrix} sinx & cosx \\ -cosx & sinx \end{vmatrix}\)

By using 2×2 determinant formula, we obtain

| A | = ( \(sin^2x\)) – (\(-cos^2x\)) = \(sin^2x\) + \(cos^2x\) = 1