Prove that `sqrt(x^2+2x+1)-sqrt(x^2-2x+1)={-2, x<-1 2x,-1lt=xlt=1 2,x >1`

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

If sin^(-1) x + sin^(-1) y = pi/2 , prove that x sqrt(1-x^2) + y sqrt(1-y^2) =1 .

(1)/(sqrt(2x))+sqrt(2x)

If x =1/2 (sqrt(a/b)-sqrt(b/a)) then prove that (2asqrt(1+x^2))/(x+sqrt(1+x^2))= a +b

Prove that e^(x)+sqrt(1+e^(2x))>=(1+x)+sqrt(2+2x+x^(2))AA x in R

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

Prove that : sin^(-1) (2x sqrt(1-x^(2)) ) = 2 sin^(-1) x , -1/(sqrt(2))le x le 1/(sqrt(2)

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

Prove that : tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=(pi)/(4)+(1)/(2) cos^(-1)x^(2)

Prove that : sin^(-1) (2x sqrt(1-x^(2)))= 2 sin^(-1) x, - 1/(sqrt(2)) le x le 1/(sqrt(2))