If-and-are-the-interior-angles-of-a-triangle-find-the-value-of-determinant-tan-1-1-1-tan-1-1-1-tan-

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

If α, β and γ are the interior angles of a

triangle, find the value of

| \begin{matrix} \tan α & 1 & 1 \\ 1 & \tan β & 1 \\ 1 & 1 & \tan γ \end{matrix} |

Answered by MJS_new last updated on 27/Apr/21

2

all you need is

\tan γ = \tan (π - (α + β)) = - \tan (α + β) =

= - \frac{\tan α + \tan β}{1 - \tan α \tan β}

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