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

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

(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)

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

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

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

Number ofsolution(s) ofthe equation cos^(-1)sqrt(x)-sin^(-1)sqrt(x-1)+cos^(-1)sqrt(1-x)-sin^(-1)((1)/(sqrt(x)))=(pi)/(2)