Tangent of 195 Degrees

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Theorem

$\tan 195 \degrees = \tan \dfrac {13 \pi} {12} = 2 - \sqrt 3$

where $\tan$ denotes tangent.


Proof

\(\ds \tan 195 \degrees\) \(=\) \(\ds \map \tan {360 \degrees - 165 \degrees}\)
\(\ds \) \(=\) \(\ds -\tan 165 \degrees\) Tangent of Conjugate Angle
\(\ds \) \(=\) \(\ds 2 - \sqrt 3\) Tangent of $165 \degrees$

$\blacksquare$


Sources