(a) Given : $(\sec \alpha + \tan \alpha )(\sec \beta + \tan \beta )(\sec \gamma + \tan \gamma )$

$ = \tan \alpha \tan \beta \tan \gamma $ …$(i)$

Let $ x = (\sec \alpha – \tan \alpha )(\sec \beta – \tan \beta )(\sec \gamma – \tan \gamma )$ …$(ii)$

Multiply both equations, $(i)$ and $(ii)$, we get

$({\sec ^2}\alpha – {\tan ^2}\alpha )({\sec ^2}\beta – {\tan ^2}\beta )({\sec ^2}\gamma – {\tan ^2}\gamma )$

$ = x.(\tan \alpha \tan \beta \tan \gamma )$

$ \Rightarrow x = \frac{1}{{\tan \alpha \tan \beta \tan \gamma }}$

$\therefore x = \cot \alpha \cot \beta \cot \gamma $