If `x=(sqrt(2a+1)+sqrt(2a-1))/(sqrt(2a+1)-sqrt(2a-1))`, prove that `x^(2)-4ax+1=0`

If x=(sqrt(a+1)+sqrt(a-1))/(sqrt(a+1)-sqrt(a-1)) , using properties of proportion show that x^(2)-2ax+1=0

If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha, then prove that x^2=sin2alpha

If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha, then prove that x^2=sin2alpha

lim_(xrarr0) (sqrt(x+1)+sqrt(x+4)-3)/(sqrt(x+2)-sqrt2)

lim_(xrarr0) (sqrt(1+x^2)- sqrt(1+x))/(sqrt(1+x^3)-sqrt(1+x))

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

x=sqrt(1+2sqrt(1+3sqrt(1+4sqrt(1+...

If y sqrt(x^(2)+1)= log (sqrt(x^(2)+1)-x) , prove that (x^(2)+1)(dy)/(dx) +xy+1=0 .

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