Secant of Angle plus Full Angle

Theorem

$\sec \left({x + 2 \pi}\right) = \sec x$


Proof

\(\ds \sec \left({x + 2 \pi}\right)\) \(=\) \(\ds \frac 1 {\cos \left({x + 2 \pi}\right)}\) Secant is Reciprocal of Cosine
\(\ds \) \(=\) \(\ds \frac 1 {\cos x}\) Cosine of Angle plus Full Angle
\(\ds \) \(=\) \(\ds \sec x\) Secant is Reciprocal of Cosine

$\blacksquare$


Also see


Sources

  • 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 5$: Trigonometric Functions: Functions of Angles in All Quadrants in terms of those in Quadrant I
This article is issued from ProofWiki. The text is available under Creative Commons Attribution-ShareAlike License unless otherwise noted. Additional terms may apply for the media files.