Prove that `cos^(-1)((sqrt(1+x)+sqrt(1-x))/(2))=(pi)/(4)-(1)/(2)cos^(-1)x`

Prove that sin^(-1) {(sqrt(1 + x) + sqrt(1 - x))/(2)} = (pi)/(4) + (cos^(-1) x)/(2), 0 lt x lt 1

Prove that sin^(-1) {(sqrt(1 + x) + sqrt(1 - x))/(2)} = (pi)/(4) + (cos^(-1) x)/(2), 0 lt x lt 1

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

Prove that: sin^(-1){(sqrt(1+x)+sqrt(1-x))/2}=pi/4+(cos^(-1)x)/2,""0 < x < 1

Prove that: sin^(-1){(sqrt(1+x)+sqrt(1-x))/2}=pi/4+(cos^(-1)x)/2,""0 < x < 1

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

Prove that cot^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/(4)+(1)/(2)cos^(-1)x

Prove That : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/4-1/2cos^(-1)x =1/(sqrt(2))ltxle1

Prove That : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/4-1/2cos^(-1)x,-1/(sqrt(2))ltxle1