If `x + sqrt(x^2-1) + 1/(x + sqrt(x^2+1)) = 20` then `x^2 + sqrt(x^4-1) + 1/(x^2 + sqrt(x^4 -1))` =

If 2x = sqrt(a) - (1)/(sqrt(a)) , then the value of (sqrt(x^(2) + 1))/(x + sqrt(x^(2) +1)) is

If x>1 and (sqrt(x+1)+sqrt(x-1))/(sqrt(x+1)-sqrt(x-1))=2 then x

Evaluate (x^2 - sqrt(1 - x^2) )^4 + (x^2 + sqrt( 1- x^2) )^4

Simplify : (a) sqrt(y+sqrt(2xy-x^(2))) + sqrt(y-sqrt(2xy-x^(2))) (b) (x+sqrt(x^2-1))/(x-sqrt(x^(2)-1)) -(x-sqrt(x^(2)-1))/(x+sqrt(x^(2)-1))

int(x^4-1)/(x^2sqrt(x^4+x^2+1))dx= sqrt(x^2+1/(x^2)+1)+C (sqrt(x^4+x^2+1))/(x^2)+C (sqrt(x^4+x^2+1))/x+C (d) none of these

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