Secant of 255 Degrees

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Theorem

$\sec 255 \degrees = \sec \dfrac {17 \pi} {12} = -\paren {\sqrt 6 + \sqrt 2}$

where $\sec$ denotes secant.


Proof

\(\ds \sec 255 \degrees\) \(=\) \(\ds \map \sec {360 \degrees - 105 \degrees}\)
\(\ds \) \(=\) \(\ds \sec 105 \degrees\) Secant of Conjugate Angle
\(\ds \) \(=\) \(\ds -\paren {\sqrt 6 + \sqrt 2}\) Secant of $105 \degrees$

$\blacksquare$


Sources