1. Tardigrade
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  4. Let the function f(x)=(arc cot (x/2)+arc cot (x/3)/arc tan (x)2+arc tan (x)3, then f(1) is equal to

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Q. Let the function $f(x)=\frac{{arc\,\cot} \frac{x}{2}+{arc \,\cot} \frac{x}{3}}{arc\,\tan \frac{x}{2}+arc\,\tan \frac{x}{3}}$, then $f(1)$ is equal to

Inverse Trigonometric Functions

Solution:

We have, $f(1)=\frac{\cot ^{-1} \frac{1}{2}+\cot ^{-1} \frac{1}{3}}{\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{3}}$
$=\frac{\tan ^{-1} 2+\tan ^{-1} 3}{\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{3}}$
$=\frac{\frac{3 \pi}{\frac{4}{4}}}{4}=3$