Question

Prove that `|(sec^2theta, tan^2theta, 1),(tan^2theta, sec^2theta, -1),(38, 36, 2)|` = 0

Answer 1

Let Δ = `|(sec^2theta, tan^2theta, 1),(tan^2theta, sec^2theta, -1),(38, 36, 2)|`

Δ = `|(sec^2theta, 1 + tan^2theta, 1),(tan^2theta, sec^2theta - 1, -1),(38, 38, 2)|  "C"_2 -> "C"_2 + "C"_3`

Δ = `|(sec^2theta, sec^2theta, 1),(tan^2theta, tan^2theta, -1),(38, 38, 2)|`

`sec^2theta - tan^2theta` = 1

`sec^2theta = 1 + tan^2theta`

`sec^2theta - 1 = tan^2theta`

Δ = 0

Two columns are same.