Home
Class 11
MATHS
Prove that sqrt(x^2+2x+1)-sqrt(x^2-2x+1)...

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • LIMITS AND DERIVATIVES

    CENGAGE ENGLISH|Exercise All Questions|691 Videos
  • LOGARITHM

    CENGAGE ENGLISH|Exercise All Questions|173 Videos

Similar Questions

Explore conceptually related problems

Prove that sqrt(x^2+2x+1)-sqrt(x^2-2x+1)={-2, x 1

Prove that sqrt(x^2+2x+1)-sqrt(x^2-2x+1)={-2, x 1

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

Prove that e^x+sqrt(1+e^(2x))geq(1+x)+sqrt(2+2x+x^2)AAx in R

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

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

Prove that sqrt ((1- cos 2x)/( 1 + cos 2x )) = tan x, x in I or III quad.

Prove that tan^(-1).(1)/(sqrt(x^(2) -1)) = (pi)/(2) - sec^(-1) x, x gt 1

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

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