Let \( f \) and \( g \) be two functions defined on \( \mathbf{R} \...
Let \( f \) and \( g \) be two functions defined on \( \mathbf{R} \) such that \( f(x+y)=f(x) g(y)+g(x) f(y) \) for each \( x, y \in \mathbf{R} \). Let \( \Delta=\left|\begin{array}{lll}f(\theta+\alpha) & f(\alpha) & g(\alpha) \\ f(\theta+\beta) & f(\beta) & g(\beta) \\ f(\theta+\gamma) & f(\gamma) & g(\gamma)\end{array}\right| \) then \( \Delta \) equals
(a) \( f(\alpha) f(\beta) f(\gamma) \)
(b) \( g(\alpha) g(\beta) g(\gamma) \)
(c) \( f(\alpha) g(\alpha)+f(\beta) g(\beta)+f(\gamma) g(\gamma) \)
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