दिया है : $(\sec \alpha  + \tan \alpha )(\sec \beta  + \tan \beta )(\sec \gamma  + \tan \gamma )$

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

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

समी. $(i)$ व $(ii)$ को गुणा करने पर,

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

$ = 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 $