If f(x) and g(x) are functions such that f (x + y) = f(x) g(y) + g(x) f (y), then | array…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
If f(x) and g(x) are functions such that
f (x + y) = f(x) g(y) + g(x) f (y), then
\[\left|\begin{array}{lll} f(\alpha) & g(\alpha) & f(\alpha+\theta) \\ f(\beta) & g(\beta) & f(\beta+\theta) \\ f(\gamma) & g(\gamma) & f(\gamma+\theta) \end{array}\right|\] is independent of
f (x + y) = f(x) g(y) + g(x) f (y), then
\[\left|\begin{array}{lll} f(\alpha) & g(\alpha) & f(\alpha+\theta) \\ f(\beta) & g(\beta) & f(\beta+\theta) \\ f(\gamma) & g(\gamma) & f(\gamma+\theta) \end{array}\right|\] is independent of
- α
- β
- γ
- θ
Answer
(A) α, (B) β, (C) γ, (D) θ
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