Secant of 105 Degrees

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Theorem

$\sec 105^\circ = \sec \dfrac {7 \pi} {12} = - \left({\sqrt 6 + \sqrt 2}\right)$

where $\sec$ denotes secant.


Proof

\(\displaystyle \sec 105^\circ\) \(=\) \(\displaystyle \sec \left({90^\circ + 15^\circ}\right)\)
\(\displaystyle \) \(=\) \(\displaystyle - \csc 15^\circ\) Secant of Angle plus Right Angle
\(\displaystyle \) \(=\) \(\displaystyle - \left({\sqrt 6 + \sqrt 2}\right)\) Cosecant of 15 Degrees

$\blacksquare$


Sources