Question:
Mark the tick against the correct answer in the following:
$\tan ^{-1} 1+\tan ^{-1} \frac{1}{3}=?$
A. $\tan ^{-1} \frac{4}{3}$
B. $\tan ^{-1} \frac{2}{3}$
C. $\tan ^{-1} 2$
D. $\tan ^{-1} 3$
Solution:
To Find: The value of $\tan ^{-1} 1+\tan ^{-1} \frac{1}{3}$
Let, $x=\tan ^{-1} 1+\tan ^{-1} \frac{1}{3}$
Since we know that $\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$
$\Rightarrow \tan ^{-1} 1+\tan ^{-1} \frac{1}{3}=\tan ^{-1}\left(\frac{1+\frac{1}{3}}{1 \frac{1}{3}}\right)=\tan ^{-1} 2$
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