`cos^(-1)(sqrt((a-x)/(a-b)))=sin^(-1)(sqrt((x-b)/(a-b)))` is possible, if

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

The value of intsqrt(1+secx)dx is equal to (A) 2sin^-1(sqrt(2)sin(x/2))+c (B) 2cos^-1(sqrt(2)sin(x/2))+c (C) 2sin^-1(sqrt(2)cos(x/2))+c (D) none of these

Find : int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x))dx ,x in [0,1]

sin^(-1)sqrt(x)+cos^(-1)sqrt(1-x)=

sin^(-1)sqrt(x)+cos^(-1)sqrt(1-x)=

Evaluate: int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x))\ dx

If y=sqrt((a-x)(x-b))- (a-b)tan^(-1)sqrt((a-x)/(x-b)),t h e n d(dy)/(dx) is equal to'

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

intsqrt(x/(1-x))\ dx is equal to (a) sin^(-1)sqrt(x)+C (b) sin^(-1){sqrt(x)-sqrt(x(1-x))}+C (c) sin^(-1){sqrt(x(1-x))}+C (d) sin^(-1)sqrt(x)-sqrt(x(1-x))+C

Evaluate: int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x))dx