Find the determinant of the matrix.

Question

Find the determinant of the matrix.

[Cos x Sin x

-sin x cos x]

Answer 1

The determinant of a 2 by 2 matrix is as follows.

[a b

c d]

= a*d - c*b

So substituting the above matrix we get.

cos²(x) - (-sin²(x)) = cos²(x) + sin²(x)

I hope you get your answer which is 1

Answer 2

The determinant of a 2 by 2 matrix is as follows.

[a b

c d]

= a*d - c*b

So substituting the above matrix we get.

cos²(x) - -sin²(x) = cos²(x) - sin²(x)

Remembering trig identities.

This is simply

1