Cosecant of 105 Degrees
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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