Prove that `\sqrt{x+i\sqrt{x^4+x^2+1}}=\pm \frac{1}{\sqrt{2}}[\sqrt{x^2+x+1}+i\sqrt{x^2-x+1}]`

Prove that sqrt(x^2+2x+1)-sqrt(x^2-2x+1)={-2, x 1

lim_(x rarr1)(sqrt(x^(2)-1)+sqrt(x-1))/(sqrt(x^(2)-1))

Prove that: lim_(x rarr oo)x(sqrt(x^(2)+1)-sqrt(x^2-1))) = 1

a+1=2sqrt(a)x then (sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))=

" 2.(i) sqrt(3x+1)-sqrt(x-1)=2

Prove that cot^(-1) ((sqrt(1 + sin x) + sqrt(1 - sin x))/(sqrt(1 + sin x) - sqrt(1 - sin x))) = (x)/(2), x in (0, (pi)/(4))

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

(i)int(1)/(sqrt(x+1)+sqrt(x+2))dx

sqrt(x+2sqrt(x-1))+sqrt(x-2sqrt(x-1))>(3)/(2)