Cosine of Angle plus Straight Angle/Proof 1

Theorem

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


Proof

\(\ds \map \cos {x + \pi}\) \(=\) \(\ds \cos x \cos \pi - \sin x \sin \pi\) Cosine of Sum
\(\ds \) \(=\) \(\ds \cos x \cdot \paren {-1} - \sin x \cdot 0\) Cosine of Straight Angle and Sine of Straight Angle
\(\ds \) \(=\) \(\ds -\cos x\)

$\blacksquare$

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