Question

Evaluate \(\begin{vmatrix}-sinθ&-1\\1&sin⁡θ\end{vmatrix}\).

(a) cos^2⁡θ

(b) -cos^2⁡θ

(c) cos⁡2θ

(d) cos⁡θ

The question was posed to me in an international level competition.

My query is from Determinant topic in division Determinants of Mathematics – Class 12

Answer 1

The correct option is (a) cos^2⁡θ

The best I can explain: Expanding along R1, we get

∆=-sinθ(sinθ)-(-1)1=-sin^2⁡θ+1=cos^2⁡θ.