A) \[{{60}^{o}}\]
B) \[{{75}^{o}}\]
C) \[{{\tan }^{-1}}3\]
D) \[{{90}^{o}}\]
Correct Answer: C
Solution :
Let the third angle is \[\theta \]. In a triangle, \[\frac{\pi }{4}+{{\tan }^{-1}}2+\theta =\pi \] \[\Rightarrow \] \[\theta =\pi -\frac{\pi }{4}-{{\tan }^{-1}}2\] \[\Rightarrow \] \[\tan \theta =\tan [\pi -(\pi /4+{{\tan }^{-1}}2)]\] \[=-\tan (\pi /4+{{\tan }^{-1}}2)\] \[=-\frac{\tan \pi /4+\tan ({{\tan }^{-1}}2)}{1-\tan (\pi /4)\tan ({{\tan }^{-1}}2)}\] \[\Rightarrow \] \[\tan \theta =-\frac{1+2}{1-2}=3\] \[\Rightarrow \] \[\theta ={{\tan }^{-1}}3\]
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