Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1...

Let `tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2))` , where `|x|<1/(sqrt(3))` . Then a value of y is : (1) `(3x-x^3)/(1-3x^2)` (2) `(3x+x^3)/(1-3x^2)` (3) `(3x-x^3)/(1+3x^2)` (4) `(3x+x^3)/(1+3x^2)`

A

`(3x - x^(3))/(1 - 3x^(2))`

B

`(3x + x^(3))/(1 - 3x^(2))`

C

`(3x - x^(3))/(1 + 3x^(2))`

D

`(3x + x^(3))/(1 + 3x^(2))`

Verified by Experts

The correct Answer is:

A

Similar Questions

Explore conceptually related problems

The result tan^(-1)x-tan^(-1)y=tan^(-1)((x-y)/(1+xy)) is true when value of xy is _____

Sovle tan^(-1)2x+tan^(-1)3x=(pi)/4

If sin^(-1)((2a)/(1+a^(2)))+cos^(-1)((1-a^(2))/(1+a^(2)))=tan^(-1)((2x)/(1-x^(2))) where a, x in[0,1] , then the value of x is ______

Prove that: tan^(-1)x+tan^(-1)(1/x)=pi/2

Solve for x : tan^(-1)(x-1)+tan^(-1)x+tan^(-1)(x+1)=tan^(-1)3x

2 tan ( tan^(-1)(x)+ tan^(-1)(x^(3))) " where " x in R - {-1,1} is equal to

Prove that, tan^(-1)x+"tan"^(-1)(2x)/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|lt1/sqrt3