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

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

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

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

Prove the following : sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,x in[-1/sqrt2,1/sqrt2]

Prove the following: sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2))

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

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

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

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))

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))