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

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 lt x lt 1

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

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

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

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

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

Prove that : sin^(-1) (2x sqrt(1-x^(2)))= 2 sin^(-1) x, - 1/(sqrt(2)) le x le 1/(sqrt(2))

Prove that : sin^(-1) (2x sqrt(1-x^(2)) ) = 2 sin^(-1) x , -1/(sqrt(2))le x le 1/(sqrt(2)

Prove that: cot^(-1)((sqrt(1+sin x)+sqrt(1-sin x))/(sqrt(1+sin x)-sqrt(1-sin x)))=(x)/(2),x in(0,(pi)/(4))