Without expanding, show that : Δ = |(cosec^2θ,cot^2θ,1)(cot^2θ,cosec^2θ,-1)(42,40,2)|

Question

Without expanding, show that:

\(\Delta=\begin{vmatrix} cosec^2\,\theta & cot^2\,\theta & 1 \\[0.3em] cot^2\,\theta & cosec^2\,\theta & -1 \\[0.3em] 42 & 40 & 2 \end{vmatrix}\)

Answer 1

Given,

\(\Delta=\begin{vmatrix} cosec^2\,\theta & cot^2\,\theta & 1 \\[0.3em] cot^2\,\theta & cosec^2\,\theta & -1 \\[0.3em] 42 & 40 & 2 \end{vmatrix}\)