Tangent Function is Odd

From ProofWiki
Jump to navigation Jump to search

Theorem

For all $x \in \C$ where $\tan x$ is defined:

$\map \tan {-x} = -\tan x$

That is, the tangent function is odd.


Proof

\(\displaystyle \map \tan {-x}\) \(=\) \(\displaystyle \frac {\map \sin {-x} } {\map \cos {-x} }\) Tangent is Sine divided by Cosine
\(\displaystyle \) \(=\) \(\displaystyle \frac {-\sin x} {\cos x}\) Sine Function is Odd; Cosine Function is Even
\(\displaystyle \) \(=\) \(\displaystyle -\tan x\) Tangent is Sine divided by Cosine

$\blacksquare$


Also see


Sources