Question

Find the determinant of the matrix A=\(\begin{bmatrix}-cos⁡θ&-tan⁡θ\\cot⁡θ &cos⁡θ \end{bmatrix}\).

(a) sin^2⁡θ

(b) sin⁡θ

(c) -sin⁡θ

(d) -sin^2⁡θ

I got this question in an online quiz.

My question is based upon Determinant topic in division Determinants of Mathematics – Class 12

Answer 1

The correct option is (a) sin^2⁡θ

To explain I would say: Given that, A=\(\begin{bmatrix}-cos⁡θ&-tan⁡θ\\cot⁡ θ&cos⁡θ \end{bmatrix}\)

|A|=\(\begin{vmatrix}-cos⁡θ&-tan⁡θ\\cot⁡θ&cos⁡θ \end{vmatrix}\)

|A|=-cos⁡θ (cos⁡θ )-cotθ(-tan⁡θ)

|A|=-cos^2⁡θ+1=sin^2⁡θ.