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A positive acute angle is divided into two parts whose tangents are $\frac{1}{2}$ and $\frac{1}{3}$. Then the angle is
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The correct answer is:
$\pi / 4$
Hints : Angle $\theta=\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{3}=\tan ^{-1}\left(\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2} \cdot \frac{1}{3}}\right)$
$=\tan ^{-1}\left(\frac{5 / 6}{5 / 6}\right)=\tan ^{-1}(1)=\pi / 4$
$=\tan ^{-1}\left(\frac{5 / 6}{5 / 6}\right)=\tan ^{-1}(1)=\pi / 4$
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