# Secant of Angle plus Straight Angle

## Theorem

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

## Proof

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

$\blacksquare$