prove that `tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}`=`(pi)/(4)-(1)/(2)cos^(-1)x`

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

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=x\ lt=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 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

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

Prove that: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2 ,

Prove that: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2 ,

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

Prove that: tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2,\ if\ pi < x <\3pi/2

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