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# Find the value of the expression in $tan^{-1} \bigg( tan \frac{3\pi}{4} \bigg)$

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Toolbox:
• $tan(\pi-x)=-tanx$
• $tan^{-1}(-1)=-\frac{\pi}{4}$
Given $tan^{-1} \bigg( tan \frac{3\pi}{4} \bigg)$:
$\large \frac{3\pi}{4}=\pi-\frac{\pi}{4}$
The given expression becomes $tan^{-1}tan \bigg[ \pi-\frac{\pi}{4} \bigg]$
Given $tan(\pi-x)=-tanx$, this becomes $tan^{-1} (-tan \frac{\pi}{4})$
$\Rightarrow\:tan^{-1}(-tan\frac{\pi}{4})=tan^{-1}(-1)=-\frac{\pi}{4}$
answered Feb 23, 2013
edited Mar 14, 2013