" (3) "tan^(-1)(sqrt(1+x^(2)))/(x)=

If x lt 0 , then prove that cos^(-1) x = pi + tan^(-1). (sqrt(1 - x^(2)))/(x)

If x lt 0 , then prove that cos^(-1) x = pi + tan^(-1). (sqrt(1 - x^(2)))/(x)

If x lt 0 , then prove that cos^(-1) x = pi + tan^(-1). (sqrt(1 - x^(2)))/(x)

Write each of the following in the simplest form: tan^(-1){sqrt(1+x^(2))-x},x in R (ii) tan^(-1){(sqrt(1+x^(2))-1)/(x)},x!=0

Differentiate the following functions with respect to x:tan^(-1){sqrt(1+x^(2))-x},x in R (ii) tan^(-1){(sqrt(1+x^(2))-1)/(x)},x!=0

find the derivative of tan^(-1)[(sqrt(1-x^(2)))/(x)] w.r.t. "tan"^(-1)(2x)/(1-x^(2)) .

Directions (Q. Nos. 16-25) Prove the following "cos"^(-1)x="tan"^(-1)[(sqrt(1-x^(2)))/(x)] .

if tan^(-1)((sqrt(1+x^(2))-1)/(x))=(pi)/(45) then:

Differentiate cos^(-1)(4x^(3)-3x) with respect to tan^(-1)((sqrt(1-x^(2)))/(x)), if 1/2

The derivative of tan^(-1)((sqrt(1+x^(2))-1)/(x)) writ.tan^(-1)x is