Question

in a right triangle ABC,right angled at B, if the ratio of AB to AC is 1:root 2, then the value of 2 tan A/1tan 2 A is

Answer 1

here is the answer. hope it is helpful plz mark as brainliest

Answer 2

Answer:

The value of $\frac{2\tan A}{1+tan^2A}$ is 1.

Step-by-step explanation:

We are given that,

In right triangle ABC, the ratio $AB : AC = 1 : \sqrt{2}$.

So, from the figure below, we get that,

$\cos A=\frac{AB}{AC}=\frac{1}{\sqrt{2}}$

i.e. $\cos A=\frac{1}{\sqrt{2}}$

$\cos A=\cos 45$

i.e. A = 45°

So, we have,

$\frac{2\tan A}{1+tan^2A}=\frac{2\tan 45}{1+tan^245}$

i.e. $\frac{2\tan A}{1+tan^2A}=\frac{2\times 1}{1+1^2}$

i.e. $\frac{2\tan A}{1+tan^2A}=\frac{2}{2}$

i.e. $\frac{2\tan A}{1+tan^2A}=1$

Hence, the value of $\frac{2\tan A}{1+tan^2A}$ is 1.