If \( \Delta=\left|\begin{array}{lll}\sin \alpha & \cos \alpha & \s...

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If \( \Delta=\left|\begin{array}{lll}\sin \alpha & \cos \alpha & \sin \alpha+\cos \beta \\ \sin \beta & \cos \alpha & \sin \beta+\cos \beta \\ \sin \gamma & \cos \alpha & \sin \gamma+\cos \beta\end{array}\right| \) then \( \Delta \) is equal to
(a) \( \sin \alpha \sin \beta \sin \gamma \)
(b) \( \cos \alpha \sec \beta \tan \gamma \)
(c) \( \sin \alpha \sin (\alpha+\beta)+\cos \alpha \cos (\gamma+\beta) \)
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