On simplifying $\cot \left(2 \tan ^{-1} x\right)$ where $|x|<1$, we get:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{1-x^2}{2 x}$
$\cot \left(2 \tan ^{-1} x\right)=\frac{1}{\tan\left(2 \tan ^{-1} x\right)}$
$=\frac{1}{\tan\left(\tan ^{-1}(\frac{2x}{1-x^2})\right)}=\frac{1-x^2}{2 x}$