Question

$\frac{A}{B} = \frac{1}{2\tan^{-1}2}$

A & B ratio is

Answer 1

$1:2\tan^{-1}2$

Answer 2

The question asks for the ratio of A to B, given the equation $\frac{A}{B} = \frac{1}{2\tan^{-1}2}$.

From the given equation, the fraction $\frac{A}{B}$ is explicitly defined as being equal to $\frac{1}{2\tan^{-1}2}$. The ratio of A to B is conventionally written as A:B, which is equivalent to the fraction $\frac{A}{B}$.

Therefore, the ratio A:B is directly given by the right-hand side of the equation. $\frac{A}{B} = \frac{1}{2\tan^{-1}2}$

This means the ratio of A to B is $1 : 2\tan^{-1}2$. Since $2\tan^{-1}2$ is an irrational number, this ratio cannot be simplified into a ratio of two integers.

The approach here is to directly interpret the given equation as defining the ratio A:B. Unlike the similar question where specific numbers (4 and 8) were provided for A and B on the left side, here A and B are the variables themselves whose ratio is being sought.