# Tangent of 225 Degrees

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## Theorem

$\tan 225^\circ = \tan \dfrac {5 \pi} 4 = 1$

where $\tan$ denotes tangent.

## Proof

 $$\displaystyle \tan 225^\circ$$ $$=$$ $$\displaystyle \tan \left({360^\circ - 135^\circ}\right)$$ $$\displaystyle$$ $$=$$ $$\displaystyle -\tan 135^\circ$$ Tangent of Conjugate Angle $$\displaystyle$$ $$=$$ $$\displaystyle 1$$ Tangent of 135 Degrees

$\blacksquare$