Tangent of 255 Degrees

From ProofWiki
Jump to navigation Jump to search

Theorem

$\tan 255 \degrees = \tan \dfrac {17 \pi} {12} = 2 + \sqrt 3$

where $\tan$ denotes tangent.


Proof

\(\ds \tan 255 \degrees\) \(=\) \(\ds \map \tan {360 \degrees - 105 \degrees}\)
\(\ds \) \(=\) \(\ds -\tan 105 \degrees\) Tangent of Conjugate Angle
\(\ds \) \(=\) \(\ds 2 + \sqrt 3\) Tangent of $105 \degrees$

$\blacksquare$


Sources