A) \[0.3\]
B) \[{{\tan }^{-1}}(1.3)\]
C) \[{{\tan }^{-1}}(0.3)\]
D) \[{{\tan }^{-1}}\left( \frac{1}{18} \right)\]
Correct Answer: C
Solution :
Given, \[\tan (x+y)=33\] \[\Rightarrow \] \[x+y={{\tan }^{-1}}(33)\] \[\Rightarrow \] \[y={{\tan }^{-1}}(33)-x\] \[[\because \,\,x={{\tan }^{-1}}(3)]\] \[\Rightarrow \] \[y={{\tan }^{-1}}(33)-{{\tan }^{-1}}(3)\] (given) \[\Rightarrow \] \[y={{\tan }^{-1}}\left( \frac{33-3}{1+33.3} \right)={{\tan }^{-1}}\left( \frac{30}{100} \right)\] \[={{\tan }^{-1}}(0.3)\]
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