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          

$\blacksquare$


Sources