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

lim_(x rarr0)(sqrt(1-x)-sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1+x))

-int(1)/(sqrt(1-x)+sqrt(1+x))(-(1)/(2sqrt(1-x))+(1)/(2sqrt(1+x)))xdx

int_( then )^( If )sqrt((1-x)/(1+x))(dx)/(x)=log((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))+2f(x)+C

If y=sin ^(-1) (xsqrt( 1-x) +sqrt(x) sqrt (1-x^(2))),then (dy)/(dx)=

(d)/(dx)[sin^(-1)(xsqrt(1 - x)- sqrt(x)sqrt(1 - x^(2)))] is equal to

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

If x= sqrt3/2 , then the value of (sqrt(1+x)+ sqrt(1-x))/(sqrt(1+x)- sqrt(1-x)) is equal to: यदि x= sqrt3/2 , (sqrt(1+x)+ sqrt(1-x))/(sqrt(1+x)- sqrt(1-x)) का मान ज्ञात करें :

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

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