Simplify
`(x + sqrt((x^(2)- 1)))^(6) + (x - sqrt((x^(2) - 1)^(6)))`

Evaluate : lim_(x to oo) sqrt(x^(2)+x +1) - sqrt(x^(2)+1)

Evaluate the following: \ (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6

Simplify : sin^-1 (x sqrt(1-x) + sqrtx sqrt(1-x^2), 0 le x le 1 .

The function f : R -> R defined as f (x) =1/2 In (sqrt(sqrt(x^2+1)+x) + sqrt(sqrt(x^2+1)-x)) is

If tan A= 1/(sqrt(x(x^2+x+1))), tan B = sqrtx/(sqrt (x^2+ x+ 1)) and tan C = sqrt(x^(-3)+x^(-2)+x^(-1)) , prove that A+B=C.

f(x)=cos^(-1)(x^(2)/sqrt(1+x^(2)))