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" 4."tan^(-1)(sqrt(1+x^(2))+x)...

" 4."tan^(-1)(sqrt(1+x^(2))+x)

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

If "tan"^(-1)(sqrt(1+x^(2))-1)/x=4^(@) then

If tan^(-1)(sqrt(1+x^(2))-1)/x=4^(0) , then

If tan^(-1) .(sqrt(1+x^(2))-1)/x = 4^(@) , then

If y="tan"^(-1) (sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(2))) show that, (dy)/(dx)=(x)/(sqrt(1-x^(4)))

Prove that "tan"^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=pi/(4)+1/(2)"cos"^(-1)x^(2) .

Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t. tan^(-1) ((x)/(sqrt(1-x^(2)))) .

Prove that tan^(-1)((sqrt(1+x^2)-1)/x)=1/2 tan^(-1)x .