Secant of 105 Degrees

Theorem

$\sec 105 \degrees = \sec \dfrac {7 \pi} {12} = -\paren {\sqrt 6 + \sqrt 2}$

where $\sec$ denotes secant.

Proof

\(\ds \sec 105 \degrees\)

\(=\)

\(\ds \map \sec {90 \degrees + 15 \degrees}\)

\(\ds \)

\(=\)

\(\ds -\csc 15 \degrees\)

Secant of Angle plus Right Angle

\(\ds \)

\(=\)

\(\ds -\paren {\sqrt 6 + \sqrt 2}\)

Cosecant of $15 \degrees$

$\blacksquare$

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