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Solve for x: tan^(-1)3x+tan^(-1)2x=pi/4...

Solve for x: `tan^(-1)3x+tan^(-1)2x=pi/4`

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))`

Text Solution

Verified by Experts

The correct Answer is:
A
Given , `tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^(2)))`,
where `|x|lt(1)/(sqrt(3))`
`rArrtan^(-1)y=tan^(-1){(x+(2x)/(1-x^(2)))/(1-x((2x)/(1-x^(2))))}`
`[becausetan^(-1)x+tan^(-1)y=tan^(-1)((x+y)/(1-xy)),xgt0,ygt0,xylt1]`
`rArrtan^(-1)y=tan^(-1)((x-x^(3)+2x)/(1-x^(2)-2x^(2)))`
`rArrtan^(-1)y=tan^(-1)((3x-x^(3))/(1-3x^(2)))rArry=(3x-x^(3))/(1-3x^(2))`
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