Secant of Angle plus Straight Angle

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Theorem

$\map \sec {x + \pi} = -\sec x$


Proof

\(\displaystyle \map \sec {x + \pi}\) \(=\) \(\displaystyle \frac 1 {\map \cos {x + \pi} }\) Secant is Reciprocal of Cosine
\(\displaystyle \) \(=\) \(\displaystyle \frac 1 {-\cos x}\) Cosine of Angle plus Straight Angle
\(\displaystyle \) \(=\) \(\displaystyle -\sec x\) Secant is Reciprocal of Cosine

$\blacksquare$


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Sources