Tangent of Angle plus Straight Angle

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Theorem

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


Proof

\(\displaystyle \tan \left({x + \pi}\right)\) \(=\) \(\displaystyle \frac {\sin \left({x + \pi}\right)} {\cos \left({x + \pi}\right)}\) Tangent is Sine divided by Cosine
\(\displaystyle \) \(=\) \(\displaystyle \frac {-\sin x} {-\cos x}\) Sine of Angle plus Straight Angle and Cosine of Angle plus Straight Angle
\(\displaystyle \) \(=\) \(\displaystyle \tan x\) Tangent is Sine divided by Cosine

$\blacksquare$


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Sources