Question

Tan-1(2tanx/1-tan^2x)

Answer 1

Answer: 2x

Step-by-step explanation:

First you have to note that formula of tan(2x)

So, tan(2x) = 2tan(x)/1-tan^2(x)

Now, tan-1(2tanx/1-tan^2x)

= tan-1(tan2x)

= 2x

There is one more rule that

tan-1(tanx) = x

Hence, Answer is (2x).....

Thank YoU!

Answer 2

$\displaystyle \sf{ {tan}^{ - 1} \bigg( \: \frac{2 \: tan x}{1 - {tan}^{2}x } \: \bigg)} = 2x$

Given :

$\displaystyle \sf{ {tan}^{ - 1} \bigg( \: \frac{2 \: tan x}{1 - {tan}^{2}x } \: \bigg)}$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ {tan}^{ - 1} \bigg( \: \frac{2 \: tan x}{1 - {tan}^{2}x } \: \bigg)}$

Step 2 of 2 :

Simplify the given expression

We use the formula

$\displaystyle \sf{ tan \: 2x = \: \frac{2 \: tan x}{1 - {tan}^{2}x } }$

Thus we get

$\displaystyle \sf{ {tan}^{ - 1} \bigg( \: \frac{2 \: tan x}{1 - {tan}^{2}x } \: \bigg)}$

$\displaystyle \sf{ = {tan}^{ - 1} \bigg( \: tan \: 2x \: \bigg)}$

$\displaystyle \sf{ = 2x}$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ tan⁻¹2 +tan⁻¹3 is..,Select Proper option from

https://brainly.in/question/5596487

2. tan⁻¹(x/y)-tan⁻¹(x-y/x+y)=... (x/y≥0),Select Proper option from the given options.

https://brainly.in/question/5596504