" 12."(sqrt(x)+(1)/(sqrt(x)))^(2)

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

(d)/(dx)[cos^(-1)(x sqrt(x)-sqrt((1-x)(1-x^(2))))]=(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))0 b.1/4c.-1/4d none of these

If x=(1)/(2)(sqrt(a)+(1)/(sqrt(a))) , then show that (sqrt(x^(2)-1))/(x-sqrt(x^(2)-1))=(a-1)/(2) .

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

(sqrt(x))^(2)-sqrt(x)-12=0

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))

Differentiate (sqrt(x^(2)+1)+sqrt(x^(2)-1))/(sqrt(x^(2)+1)-sqrt(x^(2)-1)) with respect to x:

y=sqrt(x)+(1)/(sqrt(x)), prove that 2x(dy)/(dx)=sqrt(x)-(1)/(sqrt(x))

If y=sqrt(x)+(1)/(sqrt(x)), prove that 2x(dy)/(dx)=sqrt(x)-(1)/(sqrt(x))