Cosine of 255 Degrees

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Theorem

$\cos 255^\circ = \cos \dfrac {17 \pi} {12} = - \dfrac {\sqrt 6 - \sqrt 2} 4$

where $\cos$ denotes cosine.


Proof

\(\ds \cos 255^\circ\) \(=\) \(\ds \cos \left({360^\circ - 105^\circ}\right)\)
\(\ds \) \(=\) \(\ds \cos 105^\circ\) Cosine of Conjugate Angle
\(\ds \) \(=\) \(\ds - \frac {\sqrt 6 - \sqrt 2} 4\) Cosine of 105 Degrees

$\blacksquare$


Sources