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

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  • \(tan(\pi-x)=-tanx\)
  • \(tan^{-1}(-1)=-\frac{\pi}{4}\)
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 by thanvigandhi_1
edited Mar 14, 2013 by balaji.thirumalai
 

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