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Home  >>  CBSE XII  >>  Math
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Find the value of $\tan^{-1}1+\tan^{-1}2+\tan^{-1}3.$

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  • \( tan^{-1}1=\large\frac{\pi}{4} \)
  • \( tan^{-1}x+tan^{-1}y=tan^{-1}\large\frac{x+y}{1-xy}+\pi\) if \( xy > 1\)
  • \(tan^{-1}(-1)=-\large\frac{\pi}{4}\)
By taking x=2 and y=3, \(\large\frac{x+y}{1-xy}=\large\frac{2+3}{1-6}=\large\frac{5}{-5}=-1\)
\(tan^{-1}2+tan^{-1}3=tan^{-1}\large\frac{2+3}{1-6}+\pi\)
\(=tan^{-1}(-1)+\pi=-\large\frac{\pi}{4}+\pi\)
\(and\: tan^{-1}1=\large\frac{\pi}{4} \)
 
Substituting the values in the given expression we get
\(tan^{-1}1+(tan^{-1}2+tan^{-1}3)=\large\frac{\pi}{4}+(-\large\frac{\pi}{4}+\pi)\)
\(=\pi \)

 

answered Feb 20, 2013 by thanvigandhi_1
edited Mar 19, 2013 by thanvigandhi_1
 

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