[" 6."cos^(-1)(2x-1)=],[[" (A) "2cos^(-1)x," (B) "cos^(-1)],[" (C) "2cos^(-1)sqrt(x)," (D) none "]]

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

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

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

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

If x takes negative permissible values , then sin^(-1) x= a) cos^(-1)sqrt(1-x^2) b) -cos^(-1)sqrt(1-x^2) c) cos^(-1)sqrt(x^2-1) d) pi-cos^(-1)sqrt(1-x^2)

If f(x)=cos^(-1)x+cos^(-1){(x)/(2)+(1)/(2)sqrt(3-3x^(2))} then

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

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

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