Exams › JEE Main › Maths

Let α, β, γ be real numbers with sin α, sin β, sin γ all nonzero. Define Δ = | sin²α sinα cosα cos²α | | sin²β sinβ cosβ cos²β | | sin²γ sinγ cosγ cos²γ |. What is the greatest value Δ can attain?

1. 1
2. 0
3. −1/2
4. None of these

Correct answer: 0

Solution

The determinant Δ can be evaluated using properties of sine and cosine functions, and it can be shown that the rows of the matrix are linearly dependent, leading to a determinant value of zero. This indicates that the greatest value Δ can attain is indeed 0.

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