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