Prove that :
`Sin(h^(-1)x ) = ln( x + sqrt( x^2 + 1 ))`

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

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 tan^(-1) {(x)/(a + sqrt(a^(2) - x^(2)))} = (1)/(2) sin^(-1).(x)/(a), -a lt x lt a

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

log sin sqrt(x^(2)+1)

Prove that tan^(-1){(x)/(a+sqrt(a^(2)-x^(2)))}=(1)/(2)(sin^(-1)x)/(a),-a

The function f(x) = sin| log (x + sqrt(x^2 + 1)) | is :