tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=...

`tan[2Tan^(-1)((sqrt(1+x^(2))-1)/x)]=`

A

x

B

2x

C

x/2

D

none

Text Solution

Verified by Experts

The correct Answer is:

A

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Knowledge Check

tan^(-1)(x+sqrt(1+x^(2)))=

A

`(pi)/4-1/2tan^(-1)x`

B

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

C

`(pi)/2-1/2tan^(-1)x`

D

`(pi)/4+1/2 tan^(-1)x`

(d)/(dx) {Tan ^(-1) (sqrt(1+ x ^(2))-1)/( x)}=

A

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

B

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

C

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

D

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

The derivative of Tan ^(-1)"" (sqrt(1 + x ^(2))-1)/(x) w.r.t. Tan ^(-1) "" (2x sqrt(1-x ^(2)))/(1 - 2 x ^(2))at x =0 is

A

1

B

`1//2`

C

`1//4`

D

`1//8`

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DIPTI PUBLICATION ( AP EAMET)-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE 1

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