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

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)

prove that 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)

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

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

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

Prove the followings : cos^(-1)x=2sin^(-1)sqrt((1-x)/2)=2cos^(-1)sqrt((1+x)/2)

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

Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1)x/(sqrt(1-x^(2))) (iii) "cot"^(-1)(sqrt(1-x^(2)))/x