Cosecant of 105 Degrees

Theorem

$\csc 105 \degrees = \csc \dfrac {7 \pi} {12} = \sqrt 6 - \sqrt 2$

where $\csc$ denotes cosecant.


Proof

\(\ds \csc 105 \degrees\) \(=\) \(\ds \map \csc {180 \degrees - 75 \degrees}\)
\(\ds \) \(=\) \(\ds \csc 75 \degrees\) Cosecant of Supplementary Angle
\(\ds \) \(=\) \(\ds \sqrt 6 - \sqrt 2\) Cosecant of $75 \degrees$

$\blacksquare$


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Exact Values for Trigonometric Functions of Various Angles
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