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Question Number 139484 by ZiYangLee last updated on 27/Apr/21

$$\mathrm{If}\alpha ,\beta \mathrm{and}\gamma \mathrm{are}\mathrm{the}\mathrm{interior}\mathrm{angles}\mathrm{of}\mathrm{a}$$$$\mathrm{triangle},\mathrm{find}\mathrm{the}\mathrm{value}\mathrm{of}$$$$\left|\begin{array}{ccc}\tan \alpha & 1& 1\\ 1& \tan \beta & 1\\ 1& 1& \tan \gamma \end{array}\right|$$

Answered by MJS_new last updated on 27/Apr/21

$$2$$$$\mathrm{all}\mathrm{you}\mathrm{need}\mathrm{is}$$$$\tan \gamma =\tan (\pi -(\alpha +\beta ))=-\tan (\alpha +\beta )=$$$$=-\frac{\tan \alpha +\tan \beta }{1-\tan \alpha \tan \beta }$$

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